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by Harold R. Vaughn 




A distinguished scientist’s 
lifelong pursuit of the secrets of 
“Extreme rifle accuracy ” 


Harold R. Vaughn 

Technical Library 
US Army Research Laboratoi/ 
Aberdeen Proving Gi 




vs T 



Manchester, Connecticut USA 

Rifle Accuracy Facts 

Published by: 

Precision Shooting, Inc. 

222 McKee Street 
Manchester, Connecticut 06040 

Phone: (860) 645-8776 
Fax: (860) 643-8215 


Copyright 1998 by Precision Shooting, Inc. 

T he following is a partial list of people that have contributed technical 
expertise and editing help to the author. 

Ed Adams (Civil Engineer) - Bench rest shooting. Tunnel Range. 

Roy Baty (PhD, Aero) - Mathematics, jet flow, Tunnel Range 

W. T. Atkinson (Custom Barrel Maker) - Barrel work. 

Harold Bennett (MS, EE) - Electronics, bench rest shooting. 

James K. Cole (PhD, Aero) - Shadowgraph photography. 

Robert Croll (MS, EE) - Shadowgraph technology. 

Frank A. Hemsted (Bullet Die Maker - deceased) - Die and reamer 
machine work. 

Jack E. Jackson (MD, PhD Chemistry) - Benchrest accuracy problems, 
chemistry, shadowgraph work, primary editor. 

Walter Jankowsky (Cook Bullets, deceased) - Bullet making, rail guns. 
A.A. Leiber (MS, EE, deceased) - Accuracy problems, editing. 

Rifle Accuracy Facts 

George Reis (Physicist) - Internal ballistics, instrumentation. 

Frank Tirrell (Gunsmith) - Barrel making, rail gun technology, 
benchrest shooting. 

Mark Vaughn (PhD ME) - Structural design, thread design. Tunnel Range. 
Leslie Vaughn (MS Chemistry) - Chemistry. 

Zia Rifle Club members that helped in the construction of the Tunnel 
Range (Stan Barnhart, John Winder, Allan Rittgers, Richard Henderson, 
Dick Vivian, and others), and Bill White. 


The book is dedicated to 
my wife Mary 
who supported all this work 
and edited the rough draft. 

• • 

H arold Roy Vaughn was born in 1924 at the family farm a few miles 
south of Amarillo, Texas. After graduating from high school, he 
entered Amarillo Junior College in September, 1941, to study engineering. 
He volunteered for the Army Air Corps Reserve (the beginning of the US Air 
Force) in June, 1942, and reported for duty in February, 1943. He flew 100 
combat missions in P-47’s and P-51’s from bases in New Guinea, Morotai, 
the Philippines, China, and Okinawa and was awarded the Air Medal with 
four Oak Leaf clusters and seven battle stars during his tour of duty. Colonel 
Charles Lindbergh flew several missions with Harold’s squadron as a civil- 
ian technical consultant to demonstrate how to obtain more aircraft range 
with optimum throttle and propeller speed settings. Harold returned to civil- 
ian life in January, 1946, and to Amarillo Junior College to finish the last 
semester of his sophomore year in engineering. During the summer of 1946, 
he entered the University of Colorado and received a BS in aerodynamics in 
1948 and a MS in aerodynamics in 1949. He worked at the NACA (now 
NASA) Ames Research Laboratory, Moffett Field, California, from Septem- 
ber 1949 to September 1951, where he conducted research on the aerody- 
namics of swept wings. In September 1951 he joined Sandia National 
Laboratories, Albuquerque, New Mexico as a staff member in the Aerody- 
namics Department. He was promoted to Supervisor, Aeroballistics 
Division in July 1959, a position he held until his retirement from Sandia 
National Laboratories (SNL) in 1986. This division provided the 

Rifle Accuracy Facts 

flight dynamics and the aerodynamic research and development and design 
for nuclear weapons. As supervisor of this division, he provided technical 
direction to a large staff of scientists. 

Harold is considered the “grandfather” of the aeroballistics/flight mechanics 
technology base for nuclear ordnance at SNL. In the early 1950’s he 
recognized the ballistics problem of roll-pitch resonance of tactical bombs. 
He mathematically modeled this motion and then recommended a fix of fin 
tabs, canted fins, or spin rockets to spin through the bomb pitch frequency, 
thereby avoiding divergent pitch/yaw motion. These solutions have been 
used on all nuclear bombs and sounding rocket systems at SNL. He was 
responsible for the aerodynamic design of a rocket boosted Mach 5 test 
vehicle to test baro-fuzing probes in 1957. He pioneered the use of 
computers in the field to calculate launcher settings to minimize dispersion 
for the several hundred unguided instrumentation rockets launched at Kauai 
and Johnston Island during the 1958 and 1962 high altitude nuclear tests. He 
was responsible for the aerodynamic design of the 14,000 pound Strypi rocket 
system which was developed in the fall of 1962 to boost a 560 kilogram 
nuclear warhead to an altitude of 150 kilometers at Johnston Island for the 
Checkmate event of the Dominic high altitude test series. He developed and 
published theories for analyzing reentry vehicle motion and dispersion, 
including the effects of roll resonance, heat shield thermal distortion, 
aerodynamic or inertial asymmetries, spinup, and exoatmospheric nuclear 
attack. One of these publications is extensively quoted in F. J. Regan’s 1984 
book Re-Entry Vehicle Dynamics . He developed and published a theory for 
the ballistic match (same impact point for identical launch conditions) of 
nuclear and high explosive warhead artillery shells. This theory identified 
the required matching inertial parameters which enabled the Los Alamos 
National Laboratory and the Lawrence Livermore National Laboratories to 
design the nuclear warheads. He developed and published a comprehensive 
theory for calculating forces and moments on spinning shells. In the early 
1980’s he published the numerical solution of the Navies-Stokes equations to 
predict the fluid motion inside a spinning nutating cylinder using the Cray 
super-computer. This first theoretical solution explained the flight instabili- 
ties of spin-stabilized, liquid-filled artillery shells. He also initiated many 
other programs such as (1) pioneering the use of computers to obtain com- 
plete trajectory calculations for bombs, shells, rockets, reentry vehicles, etc. 
(2) working with the SQL Field Test organization to develop a miniaturized 


About the Author 

3-axis system for use on-board test vehicles to measure angular motion which 
is telemeter to a ground station and (3) conceiving of and developing the 
SQL Flight Simulation Laboratory. 

Harold received the 1974 American Institute of Aeronautics and Astronau- 
tics Mechanics and Control of Flight Award. The award was “for his funda- 
mental contributions to the understanding of the flight mechanics of reentry 
vehicles, rockets, bombs and shells, together with his innovations in their 
aerodynamic design for stability and minimum dispersion in transonic flight.” 
He received the Outstanding Civilian Service Award from the U. S. Depart- 
ment of the Army in 1976 for solving a serious ballistics problem with the 
M422 shell. Movement of parts inside the shell caused a large undamped 
nutational motion that increased the drag, thereby markedly decreasing the 
range. He received the Department of Energy “Award of Excellence” from 
Major General W. W. Hoover in 1982 for significant contributions to the 
nuclear weapons program for “Ballistic Similitude” of artillery shells. 

Harold has many hobbies — big game hunting, oil painting, photography, 
electronics, skiing, fly fishing, gardening, ultralight aircraft, and precision 
shooting. His advancing years have made some of these hobbies fond memo- 
ries but he still pursues the less physically demanding ones. Behind his desk 
in his spacious study hangs a majestic elk, originally number 13 in the book. 
A grand slam on sheep adorns the fireplace wall. Numerous other big game 
trophies decorate the study. A small, well equipped photographic darkroom 
opens off of his study. A short hallway leads to a shop at the back of his 
garage that contains a Clausing lathe and vertical mill plus numerous other 
pieces of equipment. This well equipped shop is constantly used for projects 
related to precision shooting. 

Jack E. Jackson 


Rifle Accuracy Facts 


Chapter Page 

Acknowledgments i 

About the Author iii 

Table of Contents vii 

1 Introduction 1 

Contains data on the accuracy to be expected from different types 
of rifles and background information on why and how this work 
was done. 

2 Internal Ballistics 7 

Methods of measuring chamber pressure are discussed and the 
complete internal ballistics of a representative cartridge (270 Winches- 
ter) are measured experimentally for use in later chapters. Such things 
as bullet engraving force, different powders, and cartridge case failure 
are discussed. 

Rifle Accuracy Facts 



3 Chamber And Throat Design 33 

Methods of machining chambers and throats and their effects on 
accuracy are discussed. Various types of rifling and barrel problems 
are analyzed. 

4 Barrel Vibration 41 

Detailed measurements and theoretical calculations of barrel vibration 
are presented along with methods of reducing barrel vibration. 

The effect of barrel vibration is measured on sporters, bench rest, 
and rail guns. 

5 Scope Sight Problems 91 

Scope sight and scope mount problems are investigated and some 
solutions to these problems are found. 

6 Barrel-Receiver Threaded Joint Motion 103 

It was experimentally determined that the barrel-receiver threaded joint 
moves as a result of the shock from firing. A simple solution 
to the problem is described. 

7 Muzzle Blast 123 

The effect of bullet in-bore cant and muzzle blast on dispersion were 
determined experimentally and theoretically. Methods of reducing 
dispersion from this source are presented. 

8 Bullet Core Problems 155 

Bullet core slippage due to the spin up torque is measured and found 
to be a problem. Other bullet problems are analyzed. 

9 Bullet Imbalance 169 

The static and dynamic balance of bullets is measured and the effect of 
imbalance on dispersion is evaluated theoretically and experimentally. 
The causes of bullet imbalance are discussed. 


Table of Contents 

Chapter / Appendix / Other 


10 External Ballistics 181 

The detailed motion of a bullet after leaving the muzzle is shown and 
the effect of this motion for a given initial disturbance is evaluated. 

The effect of wind, gyroscopic stability factor, and ballistic coefficient 
on the bullet’s trajectory are shown in detail. Chronograph develop- 
ment and use are discussed. Wind gages and their use is covered. 

11 Other Problems 223 

Miscellaneous problems, such as bore cleaning, bullet coating, drift 
free bullet design, case neck tension, and shooting techniques are 

Appendices / Other 

A Accelerometer Design 237 

B Barrel Vibration Computer Equations 247 

C Bullet Balance Device Design 253 

D Six Degree Of Freedom (6DOF) Computer Equations .... 261 

E Ttinnel Range Construction 265 

F Rail Gun 271 

G Shadowgraph Testing 277 

Glossary and Abbreviations 281 

References 287 

Notes 291 


Rifle Accuracy Facts 

S ome forty five years ago, when I started big game hunting, 
I became dissatisfied with the accuracy of commercial rifles. You just 
don’t want to miss after spending days and sometimes weeks looking for a 
big trophy, and then finally getting one shot at three hundred yards or more. 
Most sporting rifles are not accurate enough for these long range shots. The 
commercial rifles that I tested would shoot 5 shot groups ranging from 4 
inches to 12 inches at 300 yards, and that just isn’t good enough for a serious 
trophy hunter. 

Now, a lot of you will say that your rifle is capable of shooting more accu- 
rately than you are capable of shooting. Now I’ll buy that, if you happen to 
be one of those people that just can’t shoot because of flinching, or not being 
able to see well, or for some other reason. However, I can’t agree with this 
for the majority of shooters, because I have fired thousands of rounds through 
accurate sporters on machine rests where the only skill involved is putting 
the cross hairs of a 20 power scope on the center of the target. Invariably, I 
get about the same accuracy when I, and other folks, shoot the same gun 
from the shoulder at prone position or from a bench rest. Bench rest shooters 
have been consistently shooting better than 0.3 inch 10 shot groups at 100 
yards for years with specially made heavy rifles and carefully assembled 
ammunition, while it is rare for a sporter to shoot better than 1.5 inch 5 shot 
groups at 100 yards. This should be ample proof that most people can shoot 

Rifle Accuracy Facts 

a lot better than their guns are capable of shooting. By the early 1 960’s I had 
light weight sporters that would reliably shoot 2.5 inch groups at 300 yards, 
which is adequate for any big game hunting. This was done by replacing 
the barrel with a custom barrel chambered with my homemade reamers and 
by replacing the stock with a carefully inletted stock. 

So, from a purely practical point of view, the hunting rifle accuracy problem 
was solved as far as I was concerned. However, I couldn’t quit while I was 
ahead of the game, because of my natural curiosity as an engineer and 
professional ballistician. It is the same incentive that drives 
the bench rest shooter to put them all through the same hole in a target, ex- 
cept that I was much more interested in why bullets didn’t go through the 
same hole than doing it in competition. The bench rest people and custom 
barrel and action people made improvements almost exclusively by trial and 
error — when something works don’t change it. While this is a fairly success- 
ful approach in the end, it doesn’t really answer the questions in a factual 
manner nor suggest which factors are more or less important. With very rare 
exceptions, you can’t find anything in the literature where people have really 
measured anything and pinned something down so that you can be positive 
about it. It is usually based on someone’s guess, which may or may not be 
right. Unfortunately, most custom gunsmiths and shooters aren’t equipped 
to do anything but group testing and are unaware of the difficulty of statisti- 
cally isolating small errors. And why haven’t modern experimental and com- 
puter techniques been applied to rifle accuracy problems when they have 
been available for years? First off the military are not particularly interested 
in gilt edge accuracy in rifles. They are interested in effectiveness, which 
means reliability, rate of fire, cost, and weight (logistics). They are very in- 
terested in accuracy in the big bore stuff (cannons), but the problems are 
somewhat different. The rifle manufacturers are undoubtedly interested, but 
let’s face it, many shooters probably buy a rifle for reasons other than accu- 
racy, and this kind of research would be very expensive when done in a large 
research laboratory. Consequently, the only way that this thing can get done 
is for someone to do it on an amateur basis (no pay), who has an extensive 
background and experience in internal and external ballistics, electronics, 
mechanical design, machine work, shop equipment, shooting, and a lot of 
free time. Well, I retired after 37 years of solving all types of projectile prob- 
lems and decided to take a shot at it. 


Chapter 1: Introduction 

The general approach in this book is to report experimental measurements 
that are conclusive wherever possible, and where it is not possible, theory 
and computer solutions are used. Guesses as to the cause of some phenom- 
ena that defy obtaining conclusive evidence will occasionally be given, but 
they will be clearly stated as guesses. While the author is certain that most of 
the major causes of inaccuracy have been isolated, evaluated and minimized 
by redesign in this work, it is also clear that every problem has not been 
solved. An attempt has been made to write this book so that it can be under- 
stood by those with little or no formal technical training. Don’t be dismayed 
by the few equations that have been included for the benefit of my scientific 
colleagues that may want to know exactly what was done. All theory is 
explained in simple physical language, so you can skip the equations and 
still understand what has been done. 

The reader should note that I have used the words accuracy, precision, and 
group size in this book. Strictly speaking they mean different things. Accu- 
racy describes the ability of a rifle to hit a given spot on a target, while preci- 
sion and group size means the ability to shoot a small group any place on a 
target. Precision is a term used by bench rest shooters to describe a small 
group. I have used these terms somewhat indiscriminately because I feel 
that you can’t have accuracy without having a small group size. 

Before getting into the nitty-gritty of rifle accuracy, we need to have some 
rough idea of the attainable accuracy of commercial sporter rifles in reason- 
able weights. I consider any rifle over eight pounds to be too heavy to be 
considered a standard sporter. Table 1 shows the data on the accuracy of 
several rifles that was obtained from the “Rifleman” and other references 
over a period of years. The data are the results of several 5-shot groups, and 
the most accurate load is presented for each rifle. The rifles have been di- 
vided into four classes-standard sporter, heavy sporter, bench rest and rail 
gun. The main point is that the typical maximum group size is about 2 inches 
and the typical average group size is about 1 .5 inches for a standard sporter. 
My experience with this class of rifle, which started in the middle 1940’s, 
indicates that this level of performance is typical. It is also typical of the 
Remington 721 that I have chosen for the investigation. The table also indi- 
cates that heavy rifles are usually more accurate than light ones, which doesn’t 
surprise me, and shouldn’t surprise the reader. It also indicates that some 
of these cartridges, such as the 6mm PPC, are more accurate than others. 


Rifle Accuracy Facts 

During the course of my research we will discover the cause of most of these 
differences. I wouldn’t get too excited about the either good or bad perfor- 
mance of a particular sporter in Table 1 , because you have to remember that 
these rifles were fired by different people using different sights and ammuni- 
tion under different conditions. The data should be viewed as simply a rough 
indication of what to expect. 


Summary Of Commercial Rifle Accuracy 

(5 shot group size at 100 yards) 







Size (inches) 



Standard Sporter 

Antonio Zoli, AZ1900 

308 Win 





Winchester, M70 

270 Wby 











McMillan Signature 

308 Win 





Dumoulin Diane 

270 Win 











Sako, PPC Repeater 






Weatherby, VGX 

270 Wby 





Ruger, Mod 77 

223 Rem 








Heavy Sporter 

Sako, Six 






Winchester, M70 

222 Rem 





Parker Hale, Mod 87 

308 Win 





Heavy Varmint Custom Gun (Bench Rest) 

Kelby Action, Hart Barrel by Jim Borden, 6mm PPC, 13.5# 0.20 

Rail Gun Unlimited Class 

Remington Action, Shilen Barrel by Vaughn, 6mm BR, 90# 0. 1 8 


Chapter 1: Introduction 

The reader should note that the data show that while a heavy rifle is likely to 
shoot better than a light one, weight is not an overriding factor. The thing 
that makes the most consistent difference is the cartridge that is used. Notice 
that the 6mm PPC, 6mm BR, 222 Remington, and the 223 Remington gener- 
ally perform better than the other cartridges. We will find that this is a result 
of these cartridges having a smaller case diameter, which reduces bolt thrust 
force, and in addition they use lighter bullets, which results in less recoil 
force. Both bolt thrust and recoil force cause inaccuracy through barrel vi- 
bration. The case diameter of these small cases is 0.378 inches as compared 
to 0.473 inches for the standard cases, and 0.532 inches for the magnum 
cases. The smaller bench rest and varmint cases use a faster burning powder, 
which reduces the effect of muzzle blast on accuracy. 

We are going to start with a standard Remington 721 action and stock that 
has been rebarreled with a Douglas Premium barrel and chambered in the 
270 Winchester cartridge. The 270 was chosen, because it is not noted for its 
accuracy and is a very commonly used cartridge in the medium case capacity 
and medium recoil range. The Remington 721 was used, because it was 
available, light, simple, strong, and has a cylindrical receiver, which is best 
for instrumentation. We start with a custom barrel, because the effects of 
thermal drift, nonconcentric chamber, and poor throat design can be mini- 
mized immediately. Every commercial rifle that the author has checked has 
had chamber and throat defects, which cause inaccuracy. These causes are 
discussed in detail in the text, and there is no reason to start with something 
that you know can cause poor performance. Later, when the research is com- 
plete, we will modify an ordinary Remington 721 in 270 Winchester and 
show that an ordinary rifle will shoot nearly as well as a varmint rifle. You 
bench rest shooters don’t get upset because the problems found in the 270 
also occur in bench rest guns, except that these effects are larger in a 270 
sporter and are easier to measure. 

At the end we will not only have an extremely accurate rifle, but we will 
understand most of the causes of inaccuracy and how to fix them. Of course, 
some accuracy problems remain to be solved and I expect to continue 
working on them. I hope the reader learns as much as I did in doing this work. 
That would make all the work worthwhile. 


Rifle Accuracy Facts 

The author recommends against trying the experiments shown in this book, 
because they could be dangerous. While the author has no reason to believe 
that any of the modifications made to the action or barrel cannot be safely 
applied in production, not enough experience has been accumulated to be 
sure that they are safe. All firing tests were made by remotely firing from a 
machine rest, which is the only safe way to conduct research of 
this type. 

Don’t fire an experimental rifle from the shoulder, because it 
could kill or maim you. 


T he best place to start in trying to isolate and evaluate the various causes 
of rifle inaccuracies is with the internal ballistics. That is, the ignition of 
the powder by the primer followed by the generation of chamber pressure by 
the burning powder, and the travel of the bullet down the barrel. When we 
get into the nitty-gritty of all these inaccuracy problems and try to either 
eliminate or minimize their effect, we are going to need to know all about the 
internal ballistics. 

Chamber Pressure Measurement 

We have to have a measured chamber pressure to determine all of the interior 
ballistics quantities that we need to know. There are three available ways to 
measure chamber pressure, (1) crusher gage, (2) piezoelectric gage, and 
(3) strain gage. Each of these methods is described. 

( 1 ) Crusher Gage - The crusher gage approach involves drilling a hole into 
the chamber which is threaded for a small cylinder with an inside diam- 
eter of about 0.2 inches. A steel piston is dropped into the cylinder, 
which is followed by the crusher gage and a top threaded cap that re- 
strains the whole thing. The crusher gage is a small copper cylinder which 
is compressed by the piston being acted on by the chamber pressure. 


Rifle Accuracy Facts 


The chamber pressure is enough to puncture a hole in the wall of the 
cartridge case. The crusher is calibrated in a static test machine by ap- 
plying a known compressive force and measuring the amount that the 
copper cylinder compresses. We won’t use this method because it is 
complicated, requires a lot of precision machine work, destroys the rifle 
for anything other than pressure testing, gives only the peak chamber 
pressure where we want a time history of the pressure, and its dynamic 
accuracy is very doubtful. Much of the pressure data shown in the older 
reloading books was obtained by this method, and is usually labeled 
CUP for either crusher or copper units of pressure. 

(2) Piezoelectric Gages - This is a newer method that is superior to the crusher 
gage. However, it requires that a pressure port be drilled into the cham- 
ber. Also, they are likely to be sensitive to gun acceleration and tem- 
perature, and, most important, they are expensive. The piezoelectric gage 
contains a small ceramic crystal that generates an electric signal when 
squeezed by the chamber pressure. This electrical voltage is propor- 
tional to the pressure and is recorded on an oscilloscope. 

Figure 2-1 - Photograph of the field test setup showing the rifle mounted on a 
machine rest and the electronic instrumentation. 


Chapter 2: Internal Ballistics 

(3) Strain Gage - The strain gage is the best for our purposes, because it is 
cheap, has a fast linear response, is nondestructive requiring no machin- 
ing, gives a time history of the pressure, and can be made insensitive to 
temperature changes. One problem is that it is difficult to calibrate, but a 
way has been developed that will be described in detail. A strain gage is 
a small piece of metal foil that is bonded to the outside of the barrel over 
the chamber. The internal chamber pressure causes the barrel to expand 
slightly, which also stretches the strain gage. When the gage is stretched 
its electrical resistance also changes. This change in resistance 
can be measured by connecting it in an electrical bridge. 
The new Oehler Model 43 Ballistics Laboratory uses this principle. 

Strain Gage Chamber Pressure Measurement 

Figure 2-1 shows the field test setup used in obtaining much of the experi- 
mental data presented in this book. The rifle is held in a machine rest that is 
clamped to the tailgate of the truck. The oscilloscope is located in the right 
front of the bed, and a portable generator is in front of the truck. Figure 2-2 
shows the experimental rifle mounted on a machine rest. The rifle is held by 
two dovetail slides which allow it to recoil when it is remotely fired by pull- 
ing a string. The wires are connected to the strain gages mounted on the 
chamber section of the barrel and the forward receiver ring. The gages on the 
forward receiver ring are used to measure moment and will be discussed later 
(Chapter 4). The location of the strain gages for measuring pressure are 
shown in Figure 2-3 where it can be seen that the two gages are mounted 
about 0.4 inches ahead of the forward receiver ring on the cylindrical section 
of the barrel, which is where the most expansion will occur. If you look 

Figure 2-2 - Experimental rifle mounted on the machine rest. 


Rifle Accuracy Facts 


Figure 2-3 - Photograph of the forward receiver ring and barrel showing two strain 
gages mounted on the barrel chamber for measuring chamber pressure and one of 
four strain gages on the receiver ring for measuring moment. 

carefully, you can also see one of the four moment gages mounted on the 
receiver ring just below the scope sight mounting block. When the chamber 
is pressurized it expands circumferentially and longitudinally, however the 
circumferential expansion or strain is much greater than the longitudinal strain, 
so we will measure the circumferential strain. A photograph of a strain gage 
is shown in Figure 2-4. The active part of the gage measures about 1/4 X 
1/8 inches. The gage is a very thin metal foil that increases in electrical 
resistance when it is stretched. This change in resistance can be converted to 
a voltage change by a strain gage bridge (Figure 2-5). A strain gage bridge is 
nothing but two resistors and two strain gages, which are also resistors, 
connected together. Six lantern batteries connected in parallel are connected 
across the bridge from top to bottom to provide a 6 volt reference voltage. 

Figure 2-4 - Photograph of a strain gage similar to those used in chamber 
pressure and receiver ring moment experimental measurements. Actual size is 
0.25 by 0.50 inches. 


Chapter 2: Internal Ballistics 

R,=R 3 = 120 OHMS 

Figure 2-5 - Circuit diagram of strain gage bridge used in chamber 
pressure measurement. 

When the two gages are stretched, the bridge is unbalanced changing the 
voltage at the two output terminals. Two strain gages are used because this 
doubles the sensitivity of the measurement and improves the accuracy. The 
voltage change can be displayed on an oscilloscope (Figure 2-6) and photo- 
graphed, after it has been amplified. This provides a permanent record of 
voltage in terms of centimeters (cm) of deflection versus time. The particu- 
lar oscilloscope (scope for short) is a Tektronix 555 (Figure 2-6), which has 
the capability of displaying two traces simultaneously. So, if we know the 
amount of scope trace vertical deflection for a given amount of chamber 

pressure, we have a direct measurement of cham- 
ber pressure as it varies with time. The horizontal 
deflection with time is done by the internal scope 
circuits. The usual approach is to use a theoretical 
calculation of the amount of strain for a given 
chamber pressure. However this is subject to a 
large error, and a more accurate experimental 
calibration will be used. 

Figure 2-6 - Photograph of the Tektronix 555 
dual trace oscilloscope used in recording 
experimental data. 


Rifle Accuracy Facts 

Figure 2-7 - Cross-section of 270 Winchester chamber and cartridge case. 

Experimental Chamber Pressure Calibration 

Figure 2-7 shows a cross-section of the chamber area of a barrel with a 270 
cartridge case, and the longitudinal location of the strain gages is indicated. 
You can see that radial expansion of the chamber will be restrained at both 
ends of the chamber with the receiver attached, because the receiver and the 
neck region are both thicker and restrain the expansion. This is what causes 
so much trouble in calibration. If the chamber section were longer so that the 
end restraints didn’t have much effect, the gages could be calibrated with a 
simple experimental test to determine the strain gage amplifier gain. We are 
going to calibrate the gages by pressurizing a modified cartridge case inside 
the chamber and noting the scope deflection while we measure the pressure 
in the case with an accurate high pressure dial gage. The cartridge case is 
attached to a 1/4 inch outside diameter (OD) steel tube with a 0.15 inch in- 
side diameter (ID). Figure 2-8 shows a photo of the case and 1/4 inch tube. 

Figure 2-8 - Photograph of the modified 270 case with a 1/4 inch OD steel tube 
attached for measuring pressure during calibration. The 1/4 inch tube extends 
down the bore and out the muzzle where it is attached to the hydraulic cylinder 
shown in Figure 2-10. 



Chapter 2: Internal Ballistics 

Figure 2-9 - Cross-section drawing of the modified case for calibration showing the 
case-tube attachment. The left end of the steel insert is larger than the inside 
diameter of the chamber neck, which prevents the internal pressure from pushing 
the insert out of the case. The insert is also soldered to the case neck. The hole in 
the head of the case with the brass plug is required for assembly. 


Figure 2-10- Photograph of Hydraulic cylinder and pressure dial gage used in 
chamber pressure calibration. 

and Figure 2-9 is a cross-section drawing of the modified case. Of course, 
the tube extends down the bore and out the muzzle where it is threaded into 
the hydraulic chamber with the 15,000 pounds/square inch (psi) gage (Figure 
2-10). The cylinder, tube, and case is filled with hydraulic fluid and as much 
air as possible is removed. The cylinder is then sealed creating a closed 
system. When the cylinder is pressurized, a direct calibration of the pressure 
versus scope deflection is obtained, and we have a pressure measurement 
that we can be sure of. This is not true of other approaches as other investi- 
gators have reported. This method can be used to at least 20,000 psi, how- 
ever, 20,000 psi gages are expensive, so I chose to use a 15,000 psi gage. The 


Rifle Accuracy Facts 

one assumption involved is that the strain gages are linear, which means that 
we are assuming that the gage response is proportional at the higher strain 
and pressure levels. Well, strain gages are known to be exceptionally linear, 
well within our ability to read scope trace deflection and the pressure from 
the dial gage, so not to worry. 

DANGER, do not conduct this experiment without adequate protection to 
the operator. A hydraulic jet at 15,000 psi is very dangerous, so enclose the 
experiment in a box. Do not use water as a working fluid, because it could 
flash vaporize if the cylinder fails, causing a violent explosion. Use a heat 
treatable steel for the cylinder, such as 4 1 L42 heat treated to at least 1 20,000 
psi. Mild steel is too weak. 

It would also be a good idea to decrease the ID of the 1/4 inch tube from 0. 15 
to 0.125 inch to improve the strength in the region of the threads on each end 
of the tube. Loctite was used as a seal on the cartridge joints and Teflon tape 
on the other joints. A new cartridge case was used, because it is softer than a 
case that has been fired and resized, and will conform to the chamber 
more quickly. 

The resulting calibration is shown in Figure 2-11, where the scope vertical 
deflection in cm (.05 volts/cm) is plotted versus the pressure measured by the 
dial gage. The points do not lie on the straight line until a pressure of about 
12,000 psi is reached, then the last three points are on the straight line through 
the origin. Lames’ equation can be used to show that a pressure of 1 2,000 psi 
is required to expand the head region of the case so that it is in hard contact 
with the inner wall of the chamber. Once the case has expanded sufficiently 
so that it is in hard contact with the chamber, the expansion of the chamber 

Figure 2-11 - Chamber pressure 
experimental calibration. At 12,000 
psi the case has expanded so that it 
is in contact with the chamber. At 
12,000 psi and above the calibration 
curve is a straight line (linear). 


Chapter 2: Internal Ballistics 

becomes proportional to the pressure and a straight line calibration results. 
This results in a voltage output of 0.285 volts (2.85 cm scope deflection) at a 
chamber pressure of 50,000 psi and a strain gage bridge supply voltage of 
6.00 volts. By repeating the experiment several times the reading accuracy 
of the data approaches a few tenths of a percent. The pressure dial gage 
accuracy is quoted by the manufacturer to be 1-1.5%. Consequently, the ac- 
curacy of the calibration is probably in the range of 1 to 2%, which amounts 
to a variation of 500- 1 000 psi at a chamber pressure level of 50,000 psi. This 
accuracy is more than adequate for our purposes and is likely more accurate 
than much of the published chamber pressure data. 

Theoretical Calibration 

There is a theoretical method of calibration, which was described by Brownell 
in 1965 (Reference 1), that uses Lames’ equation for thick-walled cylinders 
to calculate the circumferential strain at the outside surface. This strain value 
can be used with the known electronic characteristics of the strain gages and 
amplifier to arrive at a theoretical calibration. Unfortunately, Lames’ 
equation is based on the assumption that the thick-walled cylinder has an 
infinite length and constant diameter. In the real case we have a short thick- 
walled cylinder that is reinforced on one end by the forward receiver ring and 
on the other end by the tapering chamber. As a result, Lames’ equation over- 
estimates the amount of strain by roughly 20%, because the chamber section 
of the barrel is considerably stronger than a uniform thick-walled cylinder. 
This means that at a true peak chamber pressure of 50,000 psi the theoretical 
calibration would indicate a pressure of only 40,000 psi. Consequently, 
I much prefer the experimental calibration approach. 

Strain Gage Electronics 

Since someone may wish to use this method to measure chamber pressure, 
the electronic equipment and method will be briefly described. The strain 
gages are Model number HBM 6/120LY11 gages purchased from Omega 
Engineering, Inc. (l-(203)-359-1660) and are connected in abridge as is shown 
in Figure 2-4. The bridge supply voltage is furnished by four 6 volt lantern 
batteries connected in parallel and is monitored with a digital voltmeter 


Rifle Accuracy Facts 

f’S * ..■CM'**'** 
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accurate to 0.2%. The cases of the batteries are connected to the common 
ground. Any variation in this voltage directly effects the calibration in a 
proportional manner. The 120 ohm resistors should be as precise as possible. 
The leads are unshielded twisted pairs. A photo of a strain gage amplifier 

Figure 2-12 - Photograph of the strain gage bridge amplifier. 

is shown in Figure 2-12 and the circuit for the amplifier is shown in 
Figure 2-13. The gain depends on the precision of the input resistors and the 
feedback resistor and is constant to about 5 kc, which is adequate for this 
application. The 

LM101A op-amp 

chips are cheap, easy , M£6 

to use and stable, and I | 



? 0 5 X 5 MEG POT <2 

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0 9 000000 * 

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m m 0 h 0 0 99 O 0 O O O O O O OOOOO-OO* 

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# 9-0 O OS# Oto :> MJAa 1 * - 

#» a 0 0 0 0 0 OO O 0 

Figure 2-13- Circuit 
diagram of strain gage 
bridge amplifier. 


Chapter 2: Internal Ballistics 

Figure 2-14- Photograph of the scope trigger switch that starts the instrumentation. 

are made by several companies. The positive and negative 
9 volts required by the amplifier is supplied by 9 volt batteries. 

The output is adjusted to zero with the potentiometer, using a digital meter 
on the output. The output of the amplifier is connected to a Tektronics 555 
dual trace oscilloscope through 12 foot shielded cables. The 1 kw 120 volt 
AC for the whole thing is supplied by a small portable generator. 

The switch that supplies a 9 volt pulse to trigger the scope sweep is shown in 
Figure 2-14. A brass plate was soft soldered to the firing pin cocking piece, 
which interrupts an infrared light beam that shines on a photodiode. Both the 
light source and the receptor are enclosed in the plastic block shown bolted 
to the rear receiver ring. The infrared light source is a light emitting diode 
(Radio Shack No. 276-066A) that is powered by 1.5 volt batteries. The 
phototransistor (Radio Shack No. 276-145) is powered by a 9 volt battery, 
and requires no external circuitry. The white plastic block is usually covered 
with black tape to reduce stray light. The scope has an adjustable time delay 
that is used to move the pressure time history to an acceptable location on the 
scope face relative to time. 


Rifle Accuracy Facts 

The noise in the strain gage circuitry is low, about 0.2 mv. This results from 
the low impedance of the bridge (120 ohms) connected to the higher input 
impedance of the amplifier (5,000 ohms) and the relatively low output im- 
pedance of the amplifier (10,000 ohms) connected to the high input imped- 
ance of the oscilloscope (10 megohms). This has the effect of looking like a 
shorted input to the amplifier and the oscilloscope as far as noise 
is concerned. 


Now that we have suffered through all this background information — I warned 
you that you would find out more about chamber pressure measurement than 
you wanted to know — let’s look at the results. Five loads of IMR4831 
(53,55,57,59,61 grains) were tested in Remington 270 cases with 90 grain 
bullets. The scope trace is shown in Figure 2-15 for the 57 grain load. The 
upper traces are the chamber pressure and the lower traces are one channel of 
the receiver ring moment, which we will ignore for the time being. The 
major divisions on both scales are in centimeters and time is on the horizon- 

Figure 2-15 - Scope trace of chamber pressure versus time fora load of 57 grains 
of IMR4831 and a 90 grain 270 bullet. The major divisions are 1 centimeter (cm). 
Horizontal scale is set at 0.2 msec/cm. 


Chapter 2: Internal Ballistics 

Figure 2-16- Experimental chamber pressures obtained for three different powder 
loads in the Winchester 270 cartridge, using Remington cases, 90 grain Sierra 
bullets, and IMR4831 powder. The oscilloscope traces are terminated when the 
bullet exits the muzzle. 

tal scale reading from left to right at 0.2 msec. The traces are terminated, 
that is deflected off scale momentarily by a wire taped to the muzzle, which 
adds a 9 volt signal when the bullet emerges from the muzzle and contacts 
the wire. We need the bullet exit time when we compare the velocity mea- 
sured by the chronograph to that obtained from the experimental pressure 
measurement. Incidentally, the 59 grain load fills the case to the base of the 
bullet and the 61 grain load completely fills the case and requires about 0. 15 
inch compression by the bullet when the bullet is seated. The pressures 
obtained by reading the oscilloscope traces and using the experimental cali- 
bration are shown in Figure 2-16 for three powder loads. Notice that these 
curves are very regular and orderly, which is what we should expect. Sev- 
eral measurements were made which allows us to determine the variation in 
peak pressure and velocity with different powder loads. The data are shown 
in the following table. 


Rifle Accuracy Facts 


270 Winchester Case, IMR4831 Powder, 90 Grain Sierra Bullet 



Average Peak 

Peak Pressure 

Variation ±% 



Variation ±% 


























There are several things of importance to be noticed. First, the variation of 
the peak pressure about the mean is roughly 2% ( 1 000 psi) while the velocity 
variation about the mean is much bigger with light loads and as the case is 
filled more completely with powder, the velocity variation reduces to <0.6%, 
which is the resolution of the older chronograph that was used (see Chapter 
10). In other words the velocity variation is constant at the two top loads as 
far as the chronograph can tell (Figure 2-17). The symbol < means less-than. 

Figure 2-17- 

Peak chamber 
pressure for 
various IMR4831 
powder loads 
and 90 grain 
270 bullet. 





lj 50,000 

[2 40,000< 


£ 30,000 



g 20,000 






1 ^ 

54 55 56 57 58 59 60 61 



Chapter 2: Internal Ballistics 

Figure 2-18 - 
Variation of 
muzzle velocity 
extreme spread 
in percent of 
velocity for 
various IMR4831 
powder loads 
with 90 grain 270 

Graphs of the peak pressure and the velocity variation are shown in Figures 
2-17 and 2- 1 8. This data tells me that the pundits are right in that the case has 
to be fdled to a level near the base of the bullet for consistent velocities, 
which is important in achieving good accuracy. However I have never seen 
the data before to support this conclusion. The usual explanation is that the 
powder distributes itself differently when there is free space in the case, lead- 
ing to variations in powder ignition. In addition, the data tells me that an 
optimum load is probably in the neighborhood of 57 grains. A load of 58 
grains will give a peak pressure of about 60,000 psi, and a calculated peak 
tensile stress in the chamber of about 73,000 psi. This is about 40% of the 
yield stress of the barrel steel, neglecting stress concentrations (sharp 

Figure 2-19- Photograph of case heads showing change in primer appearance for 
increasing chamber pressure from left to right. 


Rifle Accuracy Facts 

corners, etc.) which are always present to some degree. Therefore, as far as 
this citizen is concerned, 58 grains would be the maximum load behind a 90 
grain bullet in this rifle. And this rifle may have lower pressures than most 
commercial rifles, because it has a throat half cone angle (0.75°) about half 
that of standard 270 chambers (1.5°). This was done with a special reamer to 
purposely ease the engraving process in order to reduce bullet distortion (more 
about this later). I have read numerous times that full case loads of 483 1 are 
safe in a 270 Winchester. A full case load of IMR4831 behind a 130 grain 
bullet would be exceedingly dangerous — so much for the pundits that guess 
without having the facts! 

I have also read that you can estimate the pressure by the condition of the 
primer. This happens to be right, but it is crude and requires a calibrated 
eyeball. To help you calibrate your eyeball, a photo of the heads of five cases 
fired with the five loads shown in Table 2, is shown in Figure 2-19. The peak 
chamber pressure increases from 40,000 psi on the left to about 70,000 psi on 
the right. You can see that the edges of the primer (Federal No. 210) and the 
edges of the firing pin indentation get sharper and more square with increas- 
ing pressure. This depends on the primer, but with experience it can be a 
rough indication of pressure level. I do not believe that firing pin indentation 
cratering means much, because it depends too much on the shape of the nose 
of the firing pin and the clearance between the pin and the hole in the bolt 
face. This type of primer cratering is more likely to occur on poorly made 
rifles, such as military rifles manufactured with excessive clearances. Figure 
2-20 shows a situation where the primer tells a great deal — you see it’s miss- 
ing!!! The pressure must have been enormous, because the primer pocket 

Figure 2-20 - Photograph of a 270 case head subjected to excessive chamber 
pressure (top) compared to a normal case (bottom). 


Chapter 2: Internal Ballistics 

was expanded from 0.210 to 0.275 inches. Compare the deformed case in 
the top of the photo with the standard 270 case in the bottom of the photo. 
You see, this fellow accidentally got a 7mm (0.284 inch diameter) bullet mixed 
with his 270 (0.277 inch diameter) bullets and tried to shoot a 7mm bullet 
through a 270 barrel. It didn’t seem possible to get this combination in the 
chamber, until I made a measurement of the chamber neck diameter and 
found out it was possible. The shooter was lucky, because the gun had a bolt 
head that completely enclosed the case head and it didn’t explode, but the 
gun was completely ruined. Anybody can make a mistake, so be careful 
when you handload. 

Calculated Interior Ballistics 

In order to get the velocity, bolt force, pressure on the base of the bullet, and 
distance the bullet moves in the barrel, we have to resort to the use of a Per- 
sonal Computer (PC) and a special internal ballistics computer code that I 
developed. We have to do this, because we need this information to isolate 
and explain the various root causes of inaccuracy. We also need to go through 
these calculations to further validate the chamber pressure measurement. This 
may seem to be an overkill as far as the chamber pressure measurement is 
concerned, but this gun nut has to be certain. Fortunately, it’s not very com- 
plicated, so hang in there. 

There are two types of pressure, static pressure and dynamic pressure. Dy- 
namic pressure (q) results from the motion of the gas and is 

q = (l/2)*Rho*V 2 

where Rho is the gas density and V is the velocity. Static pressure is the 
pressure exerted by stagnant gas. Total pressure is the sum of the two and is 
the pressure you feel when you hold your hand out the window of a speeding 
car. A long time ago a fellow named Bernoulli found out that as long as the 
gas flow velocity doesn’t exceed the speed of sound (subsonic), the total 
pressure is constant and is the sum of the static and dynamic pressures. What 
this amounts to is that the chamber pressure is equal to the total pressure or 
the stagnation pressure, because the gas velocity is negligible in the chamber. 
The static pressure on the base of the bullet is equal to the total pressure 
minus the dynamic pressure. This means that the static pressure on the base 


Rifle Accuracy Facts 

of the bullet, which drives the bullet down the barrel, decreases as the bullet 
picks up speed. Therefore, 

Pb = Pc - (l/2)*Rho*V 2 

where Pb is the static pressure acting on the base of the bullet and Pc is the 
measured chamber pressure. The gas density Rho can be obtained from the 
equation of state for a gas, which is 

P = R*Rho*Tb 

where R is a constant (1716 ft 2 /sec 2 /deg R) and Tb is the effective gas tem- 
perature (powder burn temperature) in degrees Rankine (degrees F + 459). 
We know that the temperature is about 6000°F or about 6500°R from refer- 
ence data. Consequently, we can get the pressure acting on the base of the 
bullet, subject only to the accuracy with which we know the gas temperature. 
The other thing that we don’t know about the internal ballistics is just how 
much of the powder weight is accelerated with the bullet. We know from 
theory that about half the powder weight is effectively accelerated with the 
bullet if the powder is completely burned before the bullet exits the muzzle. 
It will turn out that IMR4831 powder is so slow burning that it doesn’t all 
burn out before muzzle exit of the bullet and so about 60% of the powder is 
effectively accelerated at the speed of the bullet. Now this makes two things 
that we don’t know precisely; powder burn temperature and powder accel- 
eration fraction. However these can be determined with precision, by trial 
and error, because we know the muzzle velocity and peak chamber pressure 
at two extreme conditions, 53 and 61 grains of powder. In mathematics lan- 
guage, this is the same thing as having two equations with two unknowns, a 
problem that is easily solved. This is done by making small changes in the 
gas temperature powder mass fraction until the calculated peak chamber pres- 
sure and muzzle velocity agree with the measured values. 

However, before the computer calculations were made two relatively small 
refinements were made to the computer code. The first is the correction of 
powder burn temperature with increasing pressure. According to Reference 
2 and 3, the powder burn temperature is decreased by about 7% when the 
pressure increases from 1000 psi to 53,000 psi. The second correction, and 
the largest, is caused by the fact that the high pressure jet, that squirts out of 
the muzzle after the bullet exits, continues to accelerate the bullet for about 
15 bullet diameters (calibers). Fortunately, the U.S. Army Ballistic Research 


Chapter 2: Internal Ballistics 

Laboratories have been investigating muzzle blast effects for several years 
(Reference 4 through 8). Gion showed experimentally with an M-16 that it 
takes about 1 5 calibers for the bullet to outrun the jet after it leaves the muzzle. 
All of this is included in the computer code. Later on in Chapter 7 we show 
the same result. The effect of friction on the bullet is shown to be about 2% 
in Reference 9 and was ignored in the computer code because its effect is 
negligible. The following Table shows the results of the calculations for 
three loads (53, 57 and 61 grains). 


Comparison Of Measured To Calculated Results From 
The Internal Ballistics Code 

Powder Load 

Grains 4831 


Velocity, fps 


Velocity, fps 


Time, ms 


Time, ms 
















The velocities are in excellent agreement and the time in the barrel data are in 
fair agreement. The time in the barrel is difficult to measure, because it is 
difficult to know exactly where to start measuring the time on the pressure 
traces. Now we know for sure that the measured chamber pressures are cor- 
rect because we used the measured chamber pressures to derive the calcu- 
lated velocity. This makes it possible to obtain several calculated parameters 
that are important. 

The experimental chamber pressure and the calculated pressure acting on the 
base of the bullet for the 57 grain load are shown in Figure 2-21, where you 
can see that the bullet base pressure is considerably less than the chamber 
pressure. The bullet simply starts to outrun the gas, and this is one reason 
that your basic gun is limited in velocity. Figures 2-22 and 2-23 show the 
velocity and distance the bullet has traveled. Notice that at 0.4 ms the bullet 


Rifle Accuracy Facts 

has traveled only 3/8 inch, but the pressure on the base of the bullet 
(Figure 2-21) is about 35,000 psi and the force on the base of the bullet (Fig- 
ure 2-24) is about 2,000 pounds. This is more than enough to deform the 
bullet slightly and make it expand diametrically. This was proven experi- 
mentally by others by firing bullets from a very short barrel (6 inches) and 
recovering the bullets. This would greatly exaggerate the effect and in fact, 
these tests showed the diametrical growth was perhaps 1 0% or more. Unfor- 
tunately, no one knows how to measure this effect in a normal length barrel 
where the expansion would be much less. It could be calculated with a very 
complicated finite element computer code, but this is beyond the scope of 
this work. Bullet distortion causes inaccuracy, because it can result in a canted 
base that causes dispersion by interacting with the muzzle blast, causing the 
bullet to be deflected (Chapter 7). Bullet distortion can also cause an offset 
center of gravity (eg), which results in a tangential velocity coming from the 
high rate of spin (Figure 2-25) imparted by the rifling, and this also causes 
dispersion (Chapter 9). We will show these effects later in great detail, both 
experimentally and theoretically. 


Figure 2-21 - Comparison of chamber pressure to the pressure acting on the 
base of the 270 bullet. 


Chapter 2: Internal Ballistics 

0 0.5 1.0 1.5 


Figure 2-22 - 
Bullet velocity 
versus time in 
bore. The velocity 
is obtained by 
the measured 
pressure for the 
57 grain load 
shown in 
Figure 2-17. 

Figure 2-23 - 
Distance bullet 
has traveled 
down the barrel 
versus time in 
bore. The 
distance is 
obtained from an 
internal ballistics 
computer code 
that integrates 
the velocity. 

Rifle Accuracy Facts 



M 5000 




g 4Q0G 


§ 3000 







Figure 2-24 - Forces acting on the bolt face and on the base of the 270 bullet 
versus time in bore. Forces were calculated using the measured chamber pressure 
for a 55 grain load of IMR4831. 

Figure 2-25 - Bullet spin 
rate in cycles per second 
(cps) versus time in bore 
fora 10 inch twist. Note 
that the bullet is spinning 
at about 3400 cps 
(204,000 revolutions per 
minute) at muzzle exit. 


Chapter 2: Internal Ballistics 

Bullet Engraving Force 

A sizable force is required to push the bullet into and through the throat. I 
decided to try to measure the engraving force by pushing a 270 bullet through 
a throat with a calibrated hydraulic press. The measured engraving force was 
1200 pounds. However one has to reduce this by roughly a factor of two to 
account for the difference between static and sliding friction force. The mea- 
surement is made under the condition of static friction and sliding friction is 
about half that of static friction forces. Consequently, we end up with an 
engraving force of about 600 pounds. This translates to a pressure on the 
base of the bullet of about 10,000 psi. The chamber pressure data in 
Reference 1 indicates that a minimum chamber pressure of about 10,000 psi 
(745 pounds force) is required to push a 30 caliber 150 grain bullet through a 
barrel. My guess is that the force is proportional to the caliber and the pres- 
sure required for engraving in the throat remains more or less constant at 
about 10,000 psi. If you compare bullet motion in Figure 2-23 with the pres- 
sure in Figure 2-21 you will see that the bullet doesn’t move until a chamber 
pressure of about 10,000 psi is reached. Once the bullet has passed through 
the throat the friction force required to move the bullet in the bore is about 
80% (480 pounds) of the engraving force, although this friction force is likely 
reduced as the bullet moves faster. 

The pressure change caused by changing bullet seating depth in the case can 
also be deduced from Reference 1 for 0.308 caliber bullets. The peak cham- 
ber pressure will drop about 1000 psi for every 30 mils of additional distance 
(free run) between the bullet and contact with the lands in the throat. In other 
words, if you seat the bullet so that it has about 60 mils of free run before 
contacting the lands, the peak chamber pressure will be reduced by about 
2000 psi. This means that the chamber pressure is not very sensitive to seat- 
ing depth. I like to use somewhere between 5 and 30 mils free run for heavy 
270 or 30 caliber bullets and I like to seat light 6mm bench rest bullets in 
contact with the lands. Most bench rest shooters seat their bullets into the 
lands about 1 0 mils. This is probably more than you want to know about 
internal ballistics, but I thought it was interesting. 

Rifle Accuracy Facts 

Bullet Weight Variation 

Target shooters often weigh bullets and segregate them according to weight, 
because variations in bullet weight can cause a variation in muzzle velocity 
and bullet drop. A variation in bullet gravity drop will cause vertical disper- 
sion. The problem is that no one seems to know how much effect bullet weight 
variation has on accuracy (vertical dispersion). Well we can calculate the 
effect of variation of bullet weight on muzzle velocity and measure it experi- 
mentally. Calculations with the internal ballistics code show that the frac- 
tional change in muzzle velocity for a given fractional change in bullet weight 
can be calculated from 

(5V/V) = 0.24 * (8W/W) 


8V = change in muzzle velocity 
V = muzzle velocity 
8W = change in bullet weight 
W = bullet weight 

From this equation we can see that a variation in bullet weight of one percent 
will result in only a 0.24 percent change in muzzle velocity. The reason that 
the muzzle velocity doesn’t change as much as one might expect, is that there 
is a compensation factor involved. The heavy bullet will cause the peak pres- 
sure to be higher and to peak earlier than that of the lighter bullet, thus pro- 
viding a partially compensating effect. In order to check this theoretical 
calculation, Walter Jankowski of Cook Bullets made up some 6mm bullets in 
65 and 75 grains weight in the same jacket with identical shape. This amounts 
to a 15.4% increase in weight, and according to the equation we would ex- 
pect a 3.7% change in muzzle velocity. 1 test fired these bullets in a 6mm 
bench rest Heavy Varmint class rifle and got a variation of 3.2% in muzzle 
velocity using an Oehler 35P chronograph with six foot optical gate spacing. 
There is more about the effect of bullet weight variation on vertical 
dispersion in Chapter 10. 

Chapter 2: Internal Ballistics 

Cartridge Case Failure 

Since I have used short cartridge cases with excess headspace for experimental 
purposes, the reader may have come away with the impression that excess 
headspace is harmless and perhaps even helpful in reducing dispersion. So I 
want to dispel any notion that excess headspace, meaning more than a few 
mils, is acceptable. Repeated firing of cartridges with excess headspace will 
certainly cause case head separation, which is potentially dangerous. Recall 
that the experimental data were obtained under the condition of remote fir- 
ing. Also, these short cases were specially treated to help prevent case fail- 
ure. If you can detect any primer protrusion on a fired case, you have excess 
headspace and you need to correct it. Figure 2-26 shows four common case 
failures. The first case on the left is a standard 270 case that has suffered a 
case head separation as a result of repeated excess resizing. The second case 
from the left is a 300 magnum case that has a head separation resulting from 
excessive headspace. The third 
case from the left is a 30-06 case 

that has an axial split near the head 
of the case. This results from re- 
peatedly firing resized cases in an 
oversize chamber and is probably 
one of the most dangerous types 
of failure. Oversize chambers gen- 
erally occur in military rifles, be- 
cause they have to operate in dirty 
conditions and are not intended to 
be fired with reloads. This particu- 
lar one came from a surplus 30-06 
Springfield that I had some 40 odd 
years ago. If you have one of these 
old turkeys, it is best not to use old 
cases. The fourth and last case 
from the left is the result of firing 
a 7mm-08, which is a 308 Win- 
chester (7.62mm NATO) case 

Figure 2-26 - Photograph of four 
cartridge cases showing different 
modes of failure. Head separation 
is shown on the first two cases 
from the left. Axial split near the 
head on the third case from the 

necked down to 7mm in a 280 left. The case on the right resulted 

Remington chamber which is from firing a 7mm-08 in a 280 

much like the 30-06 chamber Remington chamber. 


Rifle Accuracy Facts 

which is shown just to the left in the figure. Well the case is about 0.44 inch 
too short for the chamber and it simply expanded to fit the chamber. Fortu- 
nately, the bullet was the right size and nobody got hurt. 
The ‘bottom line’ is — be careful. 


We now have all the internal ballistic parameters that we need to help isolate 
and minimize the other causes of inaccuracy. The force accelerating the 
bullet shown in Figure 2-24 is the same as the recoil force, the force that 
pushes the gun to the rear, and will be used later to analyze barrel 
vibration effects. 



W hile this is not intended to be a gunsmithing book, because there are 
already several good ones available, we need to describe how the cham- 
ber is machined and why it may make a difference. If the chamber or the 
throat is not concentric with the bore or if it is oversize, the bullet will have to 
rattle around (balloting) before it can line up with the bore center line and 
pass through the throat. This can cause the bullet to be deformed in an asym- 
metric manner. A throat with an overly abrupt taper can also cause bullet 
deformation. Just how this deformation takes place is a guess, but it most 
likely due to a very slight amount of in-bore canting. This will cause a center 
of gravity offset from the bore center line, which can cause dispersion. It 
also can cause the base to be canted resulting in interaction with the muzzle 
blast causing dispersion. It could also result in a tilt of the principal axis, 
which causes an error that will be discussed later. We minimize these effects 
by cutting the chamber and throat concentric with the bore and we reduce the 
slope of the throat to about one half that of standard throats. 

If you make a cast of the chamber and throat of a commercially made rifle, 
you will most likely find that they are not concentric with the bore axis — in 
other words, they are off center. A photo of front and back views of a cham- 
ber cast of a factory chamber is shown in Figure 3-1. If you look carefully at 
the top picture you can see that the rifling starts at the entrance to the throat, 


Rifle Accuracy Facts 



Figure 3-1 - Photograph of a cast of a factory production rifle throat showing offset 
chamber and throat. The cast has been rotated for the bottom photograph. 

while in the bottom photo the rifling starts at about 0. 1 8 inches from the start 
of the throat. Since the throat half cone angle is about 1 .5 degrees, the amount 
of throat offset from the bore center line can be estimated to be about 2.5 mils 
(0.0025 in). That’s several times the error that should be tolerated. This 
happens, because chambering is done very quickly in automatic machines at 
the factory, and requires the use of reamers without pilots. Any experienced 
machinist will tell you that a pilotless reamer will likely run off center and 
can greatly enlarge a hole. Figure 3-2 shows a photo of a chambering reamer 
and a separate throating reamer, where you can see the pilots on the ends of 
both reamers. The pilot is the short cylindrical section on the end that fits the 
bore very closely and guides the reamer as it cuts, so that it keeps the 

Figure 3-2 - Photograph of separate chambering and throating reamers with pilots. 


Chapter 3: Chamber and Throat Design 

chamber and throat centered with respect to the bore. The reamers are made 
of high carbon steel drill rod and are rough machined before hardening. They 
are oil quenched from 1600°F and tempered at 500°F. Then they are ground 
with a tool post grinder and sharpened by hand, and they last a long time 
without resharpening. There are adjustable stops on the shanks to control the 
final depth of cut. A piloted reamer is difficult to use in factory production, 
because chips are likely to interfere and cause the pilot to gall and seize. 
Also, you have to stop and clean the reamer often, about every 1/16 inch of 
cutting depth. You have to go very slow, operating the lathe at 60 RPM. The 
chambering operation is shown in Figure 3-3. There is nothing particularly 
new in this set up, except that it is optimized by the fact that the lathe spindle 
has a hole through it large enough to accept the barrel. You can do good work 
with a smaller lathe by holding the muzzle in the head stock and the chamber 
end in a steady rest, but it is more difficult. It takes me about two hours to 
machine a chamber and throat, after the barrel is set up in the lathe. This kind 
of time is much too long for factory production. While I haven’t measured a 

Figure 3-3 - Photograph showing the chambering operation. 


Rifle Accuracy Facts 

lot of chambers in a lot of guns from different manufacturers, I have yet to 
see a good one in a factory rifle. However, I am sure that occasionally a 
pilotless reamer does run on center and produce a more accurate chamber. 
Also, I haven’t inspected any recent factory sporters so it’s possible that the 
factories are doing a better job now, but I doubt it. 

An oversize chamber is another problem that shows up in factory rifles. This 
can result from using pilotless reamers, oversize reamers, or a poorly sharp- 
ened reamer. A factory chamber must have enough clearance to accommo- 
date cases with thick necks caused by excessive full length resizing and the 
build up of carbon and dirt in the chamber, otherwise a dangerous high pres- 
sure condition could result. They also have to accommodate a wide variety of 
commercial ammo. The case neck must be able to expand enough to release 
the bullet. The chamber body and neck that I use in the 270 have a diametri- 
cal clearance of 3 to 4 mils, and I have not had any problem. This is, in 
effect, a minimum chamber and if you are careless about the make or condi- 
tion of the hulls that you stuff in your rifle, it could cause big trouble. Bench 
rest rifles have undersize chamber necks and therefore the case necks must 
be turned down before loaded rounds will chamber. The Lapua factory 220 
Russian cases used for 6PPC bench rest rifles have neck walls that are about 
13 mils thick. The case neck is turned down so that the final case neck thick- 
ness is about 8.5 mils and the variation in thickness is kept to less than 0. 1 
mil. The loaded rounds are also carefully measured before firing to make 
sure they will chamber. The radial clearance between the neck of a loaded 
round and the chamber neck in a bench rest gun is usually only 0.4 to 0.7 mil 
(0.0004 to 0.0007 inches). They also seat the bullet into the lands, which 
helps to center the bullet. However, seating the bullet in the case so that it 
contacts the rifling in the throat also increases the peak chamber pressure, 
which is not desirable. Evidently the bench rest shooters have found that 
having the bullet centered in the bore is important, and I think they are right. 
It is not uncommon for a chamber in a military barrel to have a radial clear- 
ance of 5 mils (0.005 inches) the whole length of the chamber. 

Seating depth of the bullet in the case has an effect on just how close to the 
center the bullet will line up. Obviously, the bullet will be centered if it is in 
complete contact with the lands, however Reference 1 showed that peak cham- 
ber pressure decreases if the bullet has a free run before it contacts the lands. 
Since a minimum in peak pressure for a given load implies minimum bullet 


Chapter 3: Chamber and Throat Design 

distortion, the author prefers a seating depth that will provide about 0.010 
inches into the lands in the case of a bench rest gun with light bullets and 
about 0.020 inches of bullet free travel before the bullet contacts the lands in 
the case of a sporter shooting heavy bullets. This means that the maximum 
bullet offset in a sporter can only be about 0.2 mils (0.0002 in) with a throat 
cone half angle of 0.75 degrees. Although there is no way to prove it, a bullet 
offset of as much as a few tenths of a mil is probably small enough to mini- 
mize bullet deformation. The sketch in Figure 3-4 demonstrates what we are 

Figure 3-4 - Sketch showing the effect of seating depth on bullet centering. 

talking about. This shows a concentric throat and a chamber that is concen- 
tric but oversize. If the bullet is moved forward it will also move upward 
closer to the center line of the bore. It also shows why a shallow throat half 
angle improves bullet alignment with the bore, while allowing a satisfactory 
amount of free travel of the bullet before it starts the engraving process in the 
rifling. I have not tried throat half angles of less than 0.75 degrees, because 
bullet stripping could occur if the angle is too shallow and I doubt that a more 
shallow angle would improve the situation. I prefer a steeper slope (2.5° half 
angle) on the throat of 6mm bench guns because the short bullets seat too far 
out in the case with a shallow angle throat. Many custom bench rest guns 
have a half angle of 1 .5°. 

Standard reloading manuals describe in detail how to set seating dies for 
proper bullet seating depth. There are special tools available to bench rest 


Rifle Accuracy Facts 

shooters who carefully control seating depth. On hunting ammunition it is a 
good idea to check the final setting to make sure you can’t see rifling marks 
on a new bullet. Otherwise, the bullet may stick in the throat when you 
unload the rifle and you could have an action full of powder. That is bad 
news in the field because it is difficult to remove the powder. Obviously, this 
check should be made with an empty case or at a shooting range with 
live ammunition. 

Making really precision reamers and dies is difficult and takes a lot of time. 
It helps to make two at the same time, that way you’ve got a spare to continue 
with when you spoil the first one. It usually takes me about three days to 
make a chamber reamer. A lot of what I learned about making reamers and 
dies came from Frank A. Hemsted, one of the old time great master custom 
reloading and bullet die makers. You see, he built a set of bullet dies for me 
back in 1969 and he got curious about what I was up to and came by for a 
visit. He stayed several days and taught me a lot about machine work. He 
was around 80 years old at the time and went to the Happy Hunting Grounds 
a few years later. 

The 270 test rifle used in this book has a Douglas Premium barrel with a 
throat half cone angle of 0.75 degrees, which is about half that of a factory 
throat (1.53 degrees). This should ease the entry of the bullet into the throat 
and reduce bullet deformation. The only proof of this is that this rifle starts 
out being a little more accurate than a normal factory rifle, and the shallow 
throat angle plus a chamber centered on the bore axis are the main differ- 
ences. The other thing about a Douglas Premium barrel is that the bore is 
straight to start with and is not bent to make it straight. Straightening rifle 
barrels by bending is one of the main causes of thermal drift of the point of 
impact, because it introduces stress in the metal crystal boundaries, which 
relax with increasing temperature. Consequently, when you keep shooting 
the rifle, the barrel gets hot and it tends to return to its original bent configu- 
ration, shifting the point of impact. If the manufacturers would just refrain 
from taking excessively deep machining cuts and stop bending barrels, this 
problem would probably go away. I have found that thermal drift can be 
reduced by firing as much as a hundred rounds at a rate that keeps the barrel 
too hot to touch. I recently fired a new barrel where the point of impact drifted 
down and to the left about two inches and stabilized after about 20 rounds. 
This, in effect, is a rapid stress relieving method, because the high 


Chapter 3: Chamber and Throat Design 

temperature combined with the stresses introduced by firing expedites the 
process. Use light or medium loads, because the high temperature increases 
chamber pressure. Custom barrel makers, such as Douglas, Shilen, and oth- 
ers, stress relieve their barrel blanks by soaking them in a furnace with an 
inert atmosphere to prevent scaling at a temperature of 1020 °F. As far as I 
can determine, there is very little thermal drift in these barrels due to internal 
stress. Also, an off center bore or ramp front sights that have been brazed to 
the muzzle can cause thermal distortion. However, stress relieving won’t 
help a barrel with an off center bore or front sight ramp. There will be some 
drift due to preferential air cooling on the outside of the barrel. Preferential 
heating results from the bottom of the barrel being protected by the stock and 
from wind effects. Some unlimited class bench rest guns have an aluminum 
tube cover over the barrel, which presumably reduces the preferential 
cooling effect. 

If you wish to do your own gunsmithing there are books on the subject that 
are helpful (Reference 10, 11, 12). But be careful because guns do blow up. 
Stay away from old military actions because most of them are not very strong. 
Figure 3-5 shows a Japanese rifle that was “disassembled” by having cases 
too long for the chamber. The shooter was injured severely but recovered. 

Figure 3-5 - Photograph of a 6.5mm Ariska rifle that exploded as a result of cases 
being too long for the chamber. 

Rifle Accuracy Facts 

B arrel vibration is one of the largest contributors to rifle inaccuracy, 
however I have been unable to find any evidence of previous experi- 
mental work on this subject in the literature. Considerable work has been 
done on cannon barrel vibration by Ed Schmidt and others at the US Army 
Ballistic Research Laboratory (References 13, 14, 15, and 16), and the re- 
sults are somewhat similar to the results obtained in this work on rifles. But 
the difference in size makes it difficult to apply the cannon barrel work. The 
only explanation that one can come up with for the lack of work on this 
subject, as far as rifles are concerned, is that it is a very difficult technical 
problem that would require the effort of a large research laboratory — and 
that means a large budget. One does occasionally see an article where some- 
one discusses the problem in general terms without any factual data and of- 
ten reaches an erroneous conclusion. I recall one article where the writer 
claimed that the stepped configuration of the military Mauser rifle barrel was 
done to control or reduce barrel vibration! There is absolutely no technical 
reason to support such a contention and the stepped configuration was un- 
doubtedly used to expedite production machining. Well, in this work we are 
going to try to find out just how and why the barrel vibrates, and correct the 
causes of vibration. We will do this by measuring the moment acting on the 
forward receiver ring which causes the barrel to vibrate and then we will 
make corrections to the rifle that remove the forces that cause this driving 
moment. At the same time we will measure the barrel muzzle vibration in the 

Rifle Accuracy Facts 

vertical plane with an accelerometer just to make sure that the vertical 
vibration of the muzzle is reduced. We will also use a barrel vibration 
computer simulation code as a guide in the design of the instrumentation and 
to evaluate the effect of barrel vibration on accuracy. While the data pre- 
sented are restricted to the vertical plane, bear in mind that similar vibration 
at smaller amplitudes occurs in the horizontal plane due to the same driving 
moments or forces. 

In the course of this investigation we will find that the moments that cause 
barrel vibration result from the recoil force acting on the recoil lug, and from 
the bolt thrust acting on the bolt lugs with uneven engagement, and from forces 
generated by the cartridge case acting on a receiver that is structurally unsym- 
metrical. We will first eliminate the recoil lug moment with a special bedding 
device and then reduce the structural asymmetries in the action, resulting in a 
large reduction in the forces and moments that cause the barrel to vibrate. 

All the work on the standard and modified rifle will be conducted on a Win- 
chester 270 cartridge but is applicable to any sporter. At the end of the chap- 
ter the 6BR, 6mm Remington and the 6PPC is involved. 

Now, a note to the reader: this chapter is one of the longest and most com- 
plex in the book. However, every effort will be made to explain everything in 
physical terms so that the information should be clear to the reader without a 
technical background. So, hang in there! 

Receiver Ring Moment 

Barrel vibration is directly related to the moment in the forward receiver 
ring. Moment is nothing more than the amount of force applied multiplied 
times the distance or moment arm. For instance, if you apply a one pound 
vertical force at the muzzle (24 inch moment arm) a 24 inch-pound moment 
will result at the forward receiver ring, which can be measured with strain 
gages. In fact, that is how the gages are calibrated. You do it by applying a 
known force at a known distance, both vertically and horizontally, and read- 
ing the amount of oscilloscope deflection. In this case oscilloscope trace de- 
flection sensitivity turns out to be 240 inch-pounds/centimeter with the oscil- 
loscope sensitivity set at 0.05 volts/centimeter. Figure 4-1 shows a rear view 
of the receiver ring with the location of the four strain gages, and you can see 


Chapter 4: Barrel Vibration 






m/ \Jf 

R 3 =R 4 = 120 OHMS 
V b = 6 VOLTS 

- V, 



— o 




Figure 4-1 - Sketch showing placement of strain gages on the front receiver ring 
and the strain gage bridge for measuring receiver ring moment. 

that they are in two pairs. Each of these strain gage pairs is connected in a 
bridge circuit also shown in Figure 4-1. A strain gage pair connected in this 
manner measures the difference in strain between the two gages, which is 
proportional to the moment. Notice the difference in the circuits of the 
moment measuring bridge and the pressure measuring bridge (Figure 2-5). 
The direction of positive moment is shown by the direction of the circular 
arrows about the axes. The strain gage pairs are rotated 45 degrees to clear 
the scope mount block and the forward guard screw. However, the outputs 
from the two strain gage bridges can be combined by the oscilloscope ampli- 
fiers to obtain the moment about the horizontal and vertical axes. The mo- 
ment in the vertical plane, which is the moment about the horizontal axis, is 
equal to the sum of the A bridge and B bridge moments divided by the square 
root of two. The moment in the horizontal plane is the A moment minus the 
B moment divided by the square root of two. The oscilloscope sensitivity in 
the vertical and horizontal planes is 240 inch pounds per centimeter. The 
vertical moment is displayed on the upper trace and an upward displacement 
of the scope trace represents a moment that would push the muzzle upward. 
The horizontal moment is displayed on the lower trace and an upward dis- 
placement of the trace is equivalent to moving the muzzle to the left. 


Rifle Accuracy Facts 

Figure 4-2 - Oscillograph record showing receiver ring moment in the vertical plane 
(top) and horizontal plane (bottom). Scale is 240 inch-pounds/cm (vertical) and 0.2 
msec/cm (horizontal). 


O 400 

O 300 

> 0 

0 0.2 0.4 0.6 0.8 


Figure 4-3 - Experimental receiver ring moment for the standard rifle with no 
modifications. This represents an average case. 


Chapter 4: Barrel Vibration 

Figure 4-2 shows a sample oscilloscope record where the cartridge is fired at 
1 cm (i.e., centimeter) and the bullet exits at 8 cm on the horizontal axis. The 
peak moment in the vertical plane (top trace) is about 396 inch-pounds (1.65 
cm trace deflection) and is about 216 inch-pounds (0.9 cm trace deflection) 
in the horizontal plane. This record (Figure 4-2) is representative of a case 
where the receiver moment is near a minimum. Normally, the lower trace is 
used to record an electrical signal from a switch at the muzzle that indicates 
that bullet exit has taken place. This bullet exit signal provides an accurate 
time correlation between different records. Now, I have shown the reader 
this sample record just so you would know what the actual data looks like. 
However, it is difficult to read and interpret data in this form, so from now on 
we will convert most of the oscilloscope traces by electronic scanning to a 
form that can be plotted and manipulated by the computer. This makes it 
much easier to add the proper scales and labels and provides a much more 
readable format. This results in a small loss in resolution due to computer 
limitations. However, the improvement in readability and understanding is 
well worth this small loss in resolution. 

Figure 4-3 shows the receiver ring moment in the vertical plane for an aver- 
age case and the plot is in the new format. Note that it shows only the mo- 
ment in the vertical plane because we will concentrate on the vertical motion 
from now on. Note that the peak moment is about 450 inch-pounds. Based 
on the analysis of several hundred records, the moment can vary as much as 
± 150 inch-pounds around this nominal value of 450. In other words, the 
peak moment can vary between 300 and 600 inch-pounds with the same load. 
And also, the timing of the moment pulse can vary a small amount. This 
variation in moment is an important effect that is caused by a number of 
problems that we will investigate. Later in this chapter we will use this infor- 
mation to estimate the effect of barrel vibration on group size. 

Now, ‘the name of the game’ is to reduce this moment to as near zero as 
possible so that the barrel doesn’t vibrate. If there is no moment in the for- 
ward receiver ring, there will be nothing to drive the barrel motion. The first 
cause of the moment that we will attack is the moment due to recoil forces. 


Rifle Accuracy Facts 

Recoil Effects 

When the rifle is fired 
there is a net recoil force 
acting on the rifle action 
that is equal to the force 
acting on the base of the 
bullet, which is about 3,000 
pounds at the peak cham- 
ber pressure of 53,000 psi. 

The force acting on the 
bullet was shown in 
Figure 2-24. This force is 
transmitted to the stock by 
the recoil lug on the bottom 
of the rifle action. Since there must be an equal and opposite reaction to any 
force, the stock exerts an equal force on the recoil lug in the opposite, or 
forward direction. This force results in a recoil moment being exerted on the 
forward receiver ring tending to drive the muzzle in an upward direction. 
According to computer calculations (see Figure 4-4), a rifle barrel and ac- 
tion, not connected to the stock, will recoil about 0.10 inch during the time 
the bullet is in the barrel. The recoil moment on the receiver caused by the 
recoil lug acting on the stock can be eliminated completely by allowing the 
barrel and action to recoil freely in the stock while the bullet is in the barrel. 
Figure 4-5 shows a picture of the Recoil Isolator which uses the principle of 
flexural beams that are flexible in the axial direction but are rigid in the 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 


Figure 4-4 - Calculated distance that the 
barreled action with scope will freely recoil 
during the time that the bullet is in the barrel. 

Figure 4-5 - Photograph of the instrumental rifle mounted in the Recoil Isolator. 

Chapter 4: Barrel Vibration 

vertical and horizontal directions. The top piece is machined to fit the re- 
ceiver and is bolted to the receiver with short screws that do not interfere 
with the bottom piece, which is held in the stock by three short guard screws. 
The top piece and the receiver slide to the rear as a unit until the recoil lug 
engages a thin (90 mil) rubber bumper between the recoil lug and the bottom 
piece of the device. The purpose of the rubber bumper is to prevent peening 
of the soft aluminum surface by the recoil lug and to lessen the shock of the 
suddenly applied load to the stock. There is a small coil spring in the device 
between the recoil lug and the bottom piece that pushes forward on the recoil 
lug with a force of about 20 pounds, that keeps the recoil lug forward against 
the forward stop on the bottom piece. The two slots in the bottom surface of 
the bottom piece transmit the recoil force to the stock after the recoil lug 
recoils into the rubber bumper on the bottom piece. The bottom piece is bed- 
ded in aluminum filled epoxy (i.e., Devcon F) in the bottom of the stock 
inletting. The device is completely invisible when inserted into the stock and 
does not effect appearance. Consequently, the recoil lug will not experience 
any recoil force until it has moved rearward about 0.10 inches and the bullet 
has left the muzzle. 

It isn’t necessary for 
the action to move to 
the rear the full 0.10 
inch before the recoil 
lug strikes the rubber 
bumper, because the 
force applied to the 
recoil lug has to be 

Figure 4-6 - 
Photograph of the 
front end of the 
Recoil Isolator 
showing the details 
of the forward 
flexure. The action is 
in the forward 
position (battery) in 
the bottom photo and 
in the recoil position 
in the top photo. 


Rifle Accuracy Facts 

Figure 4-7 - Sketch showing a cross-section view of the Recoil Isolator 
laminated flexural beams. 

delayed only a few tenths of a millisecond to prevent the disturbance from 
reaching the muzzle before the bullet exits. Therefore, one need not have 
more than 0.06 inches clearance between the recoil lug and the rubber bumper. 

The flexural pivots are 0.120 inches thick and are made up of twenty four 
0.005 inch (5 mil) thick aluminum laminations. A photograph (Figure 4-6) 
of the side of the Recoil Isolator shows the end of the front flexural pivot and 
how they bend during recoil. A cross-section drawing of one of the flexural 
pivots is shown in Figure 4-7. The “C” shaped laminations are made in a die 
on a hydraulic press and 24 of them are assembled into an “I” shaped flexural 
beam which is inserted into “T” slots in the upper and lower parts of the 
device. This laminated design is very effective in allowing a large deflection 
in the axial direction without exceeding the strength of the material while 
providing essentially the same strength and rigidity in the lateral direction 
that would be obtained from a solid piece of material. In this prototype the 
laminated flexural pivots are pinned to the upper and lower pieces to prevent 
horizontal motion, but at the same time allow easy disassembly. In the pro- 
duction case the pivots could be permanently fixed to the top and bottom 
pieces by staking. Also, the front of the top piece has been milled off to 
provide clearance for the strain gage wiring, and the machining necessary for 
the magazine, safety, and bolt stop were omitted in the interest of simplicity. 


Chapter 4: Barrel Vibration 

In production, the top and bottom pieces could be injection molded, which 
should make it inexpensive. This gadget is a lot stronger than it looks, and 
unless you are one of those people that use your rifle as a crowbar it should 
be strong enough. The original design did not have the 3/32 inch rivets and 
the flexural beams showed signs of buckling under a large compressive load. 
Two rivets in the front beam and one in the rear beam greatly reduced the 
tendency to buckle without having much effect on the stiffness in the axial 
direction. The height of the “I” beams was also reduced from 0.750 to 0.700 
inches, because they turned out to be a little more flexible than the design 
calculations indicated. Reducing the height of the beams allowed adding 
some material to the lower plate in the vicinity of the recoil shoulder, which 
was marginal in strength. In spite of these minor deficiencies the original 
Recoil Isolator is still functioning properly after enduring the firing of more 
than 2000 rounds. I have gone through several designs of the Recoil Isolator 
and this is by far the most satisfactory. 

One other design that may be worth mentioning is an application of the 
design used in cannon gun mounts, which is essentially a dado slide device 
(Figure 4-8). The problem that is inherent in this approach is that the weight 
of the barrel causes the rear of the top piece of the device to move up and the 
front to move down until the flat surfaces are engaged. This motion leaves 
the canted surfaces of the dado unengaged and the action can pivot in the 
horizontal direction. Consequently, during the 4 msec (milliseconds) that it 
takes for the firing pin to travel to the primer and the bullet to travel down the 
bore, a lot of horizontal motion can take place. This effect can be reduced by 

Figure 4-8 - Photograph 
of the Dado Slide recoil 
isolator device that proved 
to be less satisfactory 
than the Recoil Isolator 
using flexural beams. 


Rifle Accuracy Facts 

adding compression springs between the top and bottom pieces, however, 
this increases the friction in the slide. In addition, there may be problems 
with the accumulation of dirt which could cause seizing of the slide. Any- 
way, I never could make this thing work satisfactorily, so it was discarded. 

The forward receiver ring moment with the Recoil Isolator installed has been 
measured and is shown in Figure 4-9 compared with the rifle without the 
Recoil Isolator. You can see that the large positive muzzle up moment that 
we attributed to recoil has completely disappeared but it has been replaced 
by a sizeable negative muzzle down moment. Needless to say, I was dumb- 
founded by this development, because I had expected the moment to decrease 
to near zero when the recoil moment was eliminated. Well, it didn’t, and 
what has happened is that we have exposed another source of moment. The 
problem is to find out where this remaining component of moment is coming 

Figure 4-9 - Experimental receiver ring moment for the standard rifle (A) and the 
standard rifle with the Recoil Isolator (B). 


Chapter 4: Barrel Vibration 

Figure 4-10 - Photograph of the rifle bolt with swiveling bolt face that proved to 
be unnecessary. 

from. However, I will tell you in advance that we will find that the negative 
moment is coming from asymmetry in the forward receiver ring. 

At first I thought it might be due to having a canted cartridge case head which 
would result in an asymmetric bolt thrust, so I built a bolt that had a swivel- 
ing bolt face (Figure 4-10) that could conform to a canted case head. The 
experimental data indicated that there was no effect. A theoretical analysis 
indicated that the brass case head is just not strong enough to transmit a large 
moment. This theory plus some other simpler experiments convinced me 
that this was not the answer. 

Another idea was that the bolt thrust was not distributed equally on the two 
bolt lugs, so I made a bolt that had a swiveling head that had to line up per- 
fectly with the receiver lugs (Figure 4-11). Again, there was no effect on the 
experimental data, so this idea was prematurely discarded. However, much 
later on I started working with another action that had not been fired very 
much, and found that the bolt lugs did not engage the receiver lugs evenly. 
When the barrel was removed, you could see that the bluing was nearly un- 
touched on the top receiver lug but was completely worn off of the bottom 
receiver lug. Smoking the bolt lugs with a candle confirmed the fact that in a 

Figure 4-11 - Photograph 
of swiveling bolt head. 
Top, bolt head with 
double rabbet joint. 
Middle, assembled bolt. 
Bottom, swivel firing pin. 

Rifle Accuracy Facts 

new action the bolt is canted front end down and rear end up as a result of the 
upward force on the sear at the rear of the bolt, which causes most of the bolt 
force to be absorbed by the bottom lug. Since the clearance between the 
receiver and the bolt body of the Remington 721 is about 8 mils the angle of 
the bolt cant is about 0.08 degrees. When I ran a smoke test on the old action 
the top and bottom lugs were evenly matched, and one wouldn’t expect the 
swivel head bolt to make any difference in the moment acting on this old 
action. At this point the “light dawned”. The old action — the one we are 
working with — had its bolt and receiver lugs accidentally lapped from firing 
thousands of rounds. After all, a lot of powder and primer residue, which is 
carbon and grit that is an effective abrasive, collects in the front of the action 
and promotes the lapping action. Also, I didn’t clean the lugs very often. We 
have recently checked the bolt lug engagement on three custom bench rest 
actions and found that on all three actions only the bottom lug is engaged. 
These custom actions were tighter than regular sporters and had a bolt-re- 
ceiver clearance of 5-6 mils. A lot of gun writers recommend deliberately 
lapping bolt lugs by applying an abrasive compound and working the action, 
which can be done, but it is an awful lot of work and wears some other parts 
of the action that you don’t want to disturb. The best way to handle this 
problem would be for the factory to machine both the bolt lugs and the bolt 
face at an appropriate angle when they make the action. I modified the new 
Remington 721 action by machining off the rear face of the bolt lugs to 0.08 
degree angle and finishing with a little lapping with the firing pin assembly 
in place. Lapping the lugs with the firing pin assembly removed (recom- 
mended by some gunsmiths) does no good at all, because the firing pin spring 
acting on the sear is what causes the rear end of the bolt to tip up in the first 
place. Correcting the bolt lug engagement requires removing about 1 mil 
from the bottom lug. At the same time I machined the 0.08 degree angle into 
the bolt face with an end mill. However, I recommend lapping the angle in 
the bolt face with an aluminum rod charged with coarse grit. The bolt is held 
at the proper angle in the lathe with a milling attachment. As a result the case 
heads stay flat after firing like they should be. If you check cases that have 
been fired a number of times in an unmodified action by placing a straight 
edge against the case head, you will find that the case heads are round. This 
is caused by the canted bolt face and supports the contention made earlier 
that the case head is too weak to cause a large moment. Just how much effect 
this canted bolt has on barrel vibration I cannot say, because I did not start 
with a new action where one could conclusively measure the effect of uneven 


Chapter 4: Barrel Vibration 



BULLETS 4 & 5 




BULLETS 1, 2, & 3 

Figure 4-12 - Target at 100 yards showing how the bullet impact shifts upward when 
the rear surface of the top bolt lug is filed off so that only the bottom bolt lug 
engages the bottom receiver lug. 

bolt lug engagement. However, I did run a qualitative test by firing a three 
shot group with even lug engagement and firing two shots after filing a few 
mils off the top lug. You can see in Figure 4-12 that the impact of the bullets 
was about two inches higher when only the bottom lug was engaged. If the 
bolt thrust were perfectly uniform from shot to shot, uneven bolt lug engage- 
ment would not cause a problem, but we know from strain gage measure- 
ment that this is not the situation. 

As a matter of interest I measured the clearance between the bolt body and 
the receiver rings in an old 98 Mauser and a pre ’64 Model 70 and both had a 
clearance of about 8 mils. It is also interesting to note that bench rest shoot- 
ers are constantly cleaning the inside of their actions so that grit never has a 
chance to accumulate on the lugs so that “accidental” lapping doesn’t have a 
chance to occur. Another thing that often occurs in bench rest shooting is 
vertical stringing of groups. The traditional medicine for this problem is to 
keep increasing the load (and pressure) until it stops, and sometimes it works. 
What is happening is the cases lengthen until they are in firm contact with the 
bolt face and this helps to keep the bolt thrust uniform. This is a dangerous 
and often unsuccessful approach to solving the problem. Some gunsmiths 


Rifle Accuracy Facts 

try to reduce the bolt clearance by sleeving the bolt. Again, you can’t reduce 
it to zero (and that is what it would take), so that approach doesn’t really 
solve the problem. It is much easier and more satisfactory to solve the prob- 
lem by removing metal off the bottom lug until even lug engagement is ob- 
tained. It should be pointed out that vertical stringing in bench rest guns can 
also be caused by high frequency barrel vibration which is discussed at the 
end of the chapter. Now we return to the original investigation. 

When I couldn’t detect a problem with the bolt, I had what I thought had to 
be the right idea. When the cartridge case is inserted, it likely lies in the 
bottom of the chamber and it will have to expand radially to fill the chamber. 
In the process of radial expansion the case head will have to rise to the center 
of the chamber and through friction on the bolt face introduce a downward 
force on the chamber. This would give rise to a negative moment and the 
whole scenario seemed logical. Well, the only thing to do was to build a bolt 
where the bolt face is supported by several slender beams that can bend in the 
lateral direction but are “hell for strong” in the axial direction. I built the bolt 
shown in Figure 4-13, which has a slotted cylindrical insert in the bolt head. 
This insert acts like a wire brush — it is very strong in the axial direction 
parallel to the “wires” but deflects easily in the lateral or perpendicular direc- 
tion allowing the cartridge case to seek its preferred position without exert- 
ing much of a lateral force. Static bench tests confirmed that it worked prop- 
erly, and I proceeded to test fire it. Sure enough, the moment disappeared 
and I was elated. However, I became suspicious when I could not reliably 
repeat the test results, and I found that the two strain gages on the bottom of 

Figure 4-13- Photograph of bolt head insert that allows lateral translation of 
cartridge case head. 


Chapter 4: Barrel Vibration 

the receiver had debonded due to oil accumulation. This is a common prob- 
lem with strain gages and you have to run checks continually to make sure 
that the gages are really working right. Unfortunately, this particular strain 
gage configuration is difficult to check and as a result I was getting bad data. 
After the gages were replaced, the negative moment returned and I had to 
discard this idea. All of this work took nearly two years and I was beginning 
to wonder if I would ever find the source or sources of the remaining mo- 
ment. Then I decided to go back and look at action asymmetry as the pos- 
sible cause. 

Action Asymmetry 

This is something that I had considered earlier but discarded because it seemed 
to act in the wrong direction. However, it turned out that receiver asymmetry 
can cause either a positive or negative moment depending on cartridge case 
dynamics. So, how does it happen. Figure 4- 1 4 is a cross-section view of the 
receiver and barrel in the vicinity of the forward receiver ring. Most of the 
bending takes place in the area between the rear face of the bolt lugs and the 
rear face of the barrel. This is, of course where the strain gages are located. 



Mi recoil lug 


Figure 4-14 - Cross-section drawing of forward receiver ring and chamber section 
of barrel showing structural asymmetries in the vertical plane. 


Rifle Accuracy Facts 

Now, notice that the receiver ring is unsymmetrical from top to bottom, and 
while it doesn’t show in this view, it is also unsymmetrical from side to side. 
First, there is a 1/4 inch threaded hole for the forward stock screw in the 
bottom of the receiver ring, and second, there is a front scope sight base 
bolted on top of the receiver. Consequently, the receiver is stronger on top 
than on the bottom. When the case head presses to the rear on the bolt face 
the receiver ring stretches more on the bottom than on the top and this corre- 
sponds to a positive (muzzle up) moment. This condition is present with a 
neck resized case or lubricated case or when there is little or no headspace. 
However, when the case is short or has significant headspace, and there is no 
lubricant present, only the primer will contact the bolt face and a large per- 
centage of the recoil force generated by the bullet is transmitted by a com- 
pressive force acting through the receiver ring. This results in the bottom of 
the receiver ring being compressed more than the top, which results in the 
negative moment shown in Figure 4-9(B). The fact that a short case 
(i.e. excessive headspace) will stick to the chamber walls and have only the 
primer contact the bolt face is confirmed in Figure 4-15. This figure shows 
the heads of three cases with headspace measurements of 15, 8, and 0 mils 
and you can see that the primer protrusion is proportional to the headspace. 
Also, the bolt thrust force was measured using the strain gages used for mea- 
suring moment by connecting them in a different arrangement. This is done 
by putting the two strain gages in opposing arms of the bridge. Figure 4-16 
shows the condition of maximum bolt thrust that occurs with zero headspace. 

Figure 4-15 - Photograph of fired 270 Winchester cases showing primer protrusion 
resulting from excess headspace of 15, 8, and 0 mils from left to right. Experiment 
is performed with special work hardened and degreased cases. 


Chapter 4: Barrel Vibration 


0 -2 .4 .6 .8 10 1.2 1.4 


Figure 4-16- Experimental measurement of maximum bolt thrust that occurs with 
either zero headspace or lubricated cases. 


Figure 4-17 - Experimental measurement of minimum bolt thrust that occurs with 
headspace greater than 5 mils and degreased cases. 


Rifle Accuracy Facts 

Figure 4-17 shows the condition of minimum bolt thrust which occurs with a 
large headspace (i.e., 10 mils). The measurements show that the maximum 
bolt thrust is about 7,500 pounds and the minimum bolt thrust is about 800 
pounds. Calculations made by multiplying the internal cross-section area of 
the case and the primer by the peak chamber pressure show that the maxi- 
mum value should be 7,200 pounds and the minimum should be 1 ,200 pounds. 
The minimum measured bolt thrust (i.e., 800 pounds) is less than the calcu- 
lated value of 1,200 pounds, because the calculation does not include the 
effect of friction between the side walls of the primer and primer pocket. 
Since the recoil force is about 3,000 pounds, the receiver ring must be in 
compression when the recoil force is at the minimum. The data in 
Figure 4-17 were obtained by firing cases that were degreased and had 
an excess headspace of 10 mils and gripped the chamber walls. In practice 
you can get just about any combination of tension or compression, depend- 
ing on the hardness, lubrication and length of the case. Well we can 
eliminate the receiver asymmetries to a great extent by making some 
simple modifications. 

Figure 4-18- Cross-section view of the receiver ring modified to reduce structural 
asymmetries in the vertical plane. 


Chapter 4: Barrel Vibration 



Figure 4-19 - Lateral cross-section view of the forward receiver ring and scope 
mount base showing modifications made to improve symmetry. 

Receiver Modifications 

The modified receiver is shown in Figure 4-18. You can see that a 1/4 inch 
hole has been drilled in the top of the receiver ring to match the guard screw 
hole in the bottom of the ring, and an 1/8 inch hole has been drilled in the left 
side to offset the vent hole on the right side of the receiver. Also, the front 
half of the front scope mount base is silver soldered to the receiver and the 
rear screw in the front base has been omitted. Now, I should tell you that the 
scope mount bases are made of steel instead of aluminum. This makes it 
possible to use a low temperature (430 °F) melting point silver braze to firmly 
attach the bases. Silver solder or braze is nearly as strong as mild steel and it 
is the only way that I have found to keep screw mounted scope sight bases 
from moving in the horizontal direction. Some of the newer rifles provide a 
direct clamping of the bases to the receiver and probably eliminate this prob- 
lem. The reader should be cautioned not to try either drilling the blank holes 
in the receiver ring or brazing the scope sight base onto the receiver, because 
both these modifications are potentially dangerous as they have not been safety 
tested. While analysis indicates that both of these modifications are safe 
enough when properly performed, the only way to really test for safety is to 
test several modified rifles to destruction. Such tests have not been performed. 
Figure 4-19 shows a cross-section view of the regular forward receiver 


Rifle Accuracy Facts 

ring and the modified receiver ring, and you can see that the unmodified 
receiver is unsymmetrical about a horizontal axis while the modified 
receiver is symmetrical. 

Later in the investigation I discovered that the scope sight has the effect of 
strengthening the top of the receiver, because it is attached to both the front 
and rear receiver rings. The solution would be to build a forward scope mount 
that would allow the scope tube to slide in the axial direction, thus preventing 
any application of a moment to the front receiver ring. Scope mounts for 
target rifles are made that allow the scope to slide in the axial direction, how- 
ever they are too bulky for a sporter. I tried a simple modification to a stan- 
dard Weaver mount that didn’t work well, so I decided to let this problem go 
for a while. Since it is only a small effect we can worry about it later. 

By now everyone must be wondering if all this work has had the desired 
effect — that is, is the receiver ring moment smaller? Well, you can see in 
Figure 4-20(B) that the forward receiver ring moment has been greatly re- 
duced to a very low level compared to the unmodified standard rifle (Figure 
4-20(A)). The average level of the moment acting on the modified rifle var- 
ies between +10 and -18 inch-pounds and it doesn’t change much between 
the two extremes of bolt thrust. When you recall that we started with a peak 
moment of +450 inch-pounds (Figure 4-3 and Figure 4-20(A)), this repre- 
sents a remarkable improvement. Consequently, barrel vibration should have 
been greatly reduced. However, I won’t be completely satisfied until we 
actually measure the vibration of the barrel at the muzzle and find out for 
sure that we have reduced it. This can be done with an instrument 
called an accelerometer. 

Acceleration Measurements 

Measuring the acceleration on the muzzle of a rifle barrel turned out to be a 
very difficult problem requiring several months of effort to obtain reliable 
data. In fact, it involved so much work that I haven’t seen before, I decided to 
include the technical details in Appendix A. Hopefully, if we avoid most of 
this technical detail at this point in the book, the reader will have a clearer 
picture of the results. However, we will have to discuss the instrumentation 
to some extent if the reader is to have a complete understanding of the data. 


Chapter 4: Barrel Vibration 

Figure 4-20 - Comparison of the measured receiver ring moment on the unmodified 
standard rifle (A) and the modified rifle with Recoil Isolator and modified receiver 
ring to achieve symmetry (B). 

An accelerometer is a device that puts out an electrical voltage that is propor- 
tional to the acceleration it is subjected to. Acceleration is nothing more than 
the rate of change of velocity. When you speed up your car you feel accelera- 
tion. The reason we want to measure acceleration is that when acceleration 
is multiplied by time you have velocity, and when velocity is multiplied by 
time you have deflection. This process is called integration and is easily 
done with an electronic circuit. Velocity and deflection are the quantities that 
we need to tell us just how the muzzle is moving. The sensing element in this 
accelerometer is a thin beam mounted parallel to the bore that is 0.4 inches 
long, 0.2 inches wide, and 0.015 inches thick. This sensing element has a 
piezoelectric film bonded to both sides of the beam, which is very sensitive 
to being stretched or compressed, and produces an electrical signal when this 
little beam bends as it is subjected to acceleration. The voltage is amplified 
by an op-amp integrated electronics chip. The output voltage of the acceler- 
ometer amplifier, which has a gain of 50, is fed to a bandpass filter which 


Rifle Accuracy Facts 

suppresses signal frequencies both below and above a frequency of 1 .25 kc 
(kilocycles). We will find out later that 1 .25 kc is the frequency of the third 
mode of vibration and that it is the predominate mode of vibration. If you 
look back at the moment data in Figure 4-2 you can see that vibration is 
composed of several frequencies including the third mode, which is the low- 
est frequency component. There are other higher frequencies present that 
have little effect on the motion. The general idea is to get rid of these high 
frequency components in the data, because they don’t contribute much to the 
actual motion, but they do obscure the part of the data that we want to see. 
The accelerometer is deliberately designed to suppress high frequencies since 
it has a natural frequency of 2 kc and is heavily damped with a 0.5 damping 
factor. The output of the bandpass filter and the integrators is recorded on the 
oscilloscope just as the moment data were. The biggest problem in making 
these accelerometer measurements is called cross-axis sensitivity. An accel- 
erometer is never made quite perfectly and as a result it not only measures 
acceleration on the intended axis but picks up some of the acceleration acting 
perpendicular to the intended axis. This means that the accelerometer is likely 
to be influenced by the large axial recoil acceleration (500 G’s) and indicate 
some small percentage of this off-axis acceleration. The bad part about this 
is that you can’t distinguish between the cross-axis effect and the vertical 
muzzle acceleration data that you are trying to measure. The best commer- 
cial accelerometers have cross-axis sensitivities of 5% and according to bench 
tests this one has 5% to 7%. That means that if the accelerometer were rig- 
idly attached to the muzzle, we could see as much as 25 to 35 G’s from this 
error source. Since the vertical acceleration at the muzzle that we are trying 
to measure is only about 25 to 30 G’s, we have a problem because the error in 
the measurement is as large as the value we want to measure. Fortunately, 
about 95% of this cross- axis effect can be eliminated by allowing the barrel 
to move with recoil while the accelerometer remains almost stationary, which 
means we will have an error of maybe 1 or 2 G’s. Figure 4-21 is a 

Figure 4-21 - 
Photograph of the 


mounted on the 
barrel near 
the muzzle. 

Chapter 4: Barrel Vibration 

photograph of the accelerometer mounted on the barrel near the muzzle. It is 
a cylinder with a hole in the center that closely fits a cylinder turned on the 
barrel for a length of 1 .5 inches. There are two spring loaded plungers lo- 
cated at ±45° from the bottom of the cylinder that force metal-to-metal con- 
tact. Consequently, friction between the barrel and cylinder is the only thing 
that can accelerate the accelerometer in the axial direction. The spring ten- 
sion is reduced to the point where there is just enough force to keep the accel- 
erometer in firm contact with the barrel when it is being vibrated at 30 G’s in 
the lateral (i.e., perpendicular to the bore) direction. Fortunately, the barrel 
only has to move to the rear about 0. 1 inch before the bullet exits the muzzle. 
A circular washer is clamped on the very end of the muzzle to prevent the 
accelerometer from sliding off the end of the barrel. In this way, we are able 
to greatly reduce the cross-axis effect. The unit of gravitational acceleration, 
which is labeled G, is 32. 16 feet/sec 2 . So now we have an accelerometer, and 
what does it tell us? 

Figures 4-22, 4-23 and 4-24 show vertical acceleration, velocity and deflec- 
tion at the muzzle for the unmodified standard rifle compared with the 
modified rifle with the Recoil Isolator and modified forward receiver ring. 

Figure 4-22 - Experimental measurements of muzzle vertical acceleration for the 
standard rifle (A) with no modifications and the rifle with Recoil Isolator and modified 
receiver ring (B). 


Rifle Accuracy Facts 

Figure 4-23 - Experimental measurements of muzzle vertical velocity for the 
standard rifle with no modifications (A) and the rifle with Recoil Isolator and 
modified receiver ring (B). 

Figure 4-24 - Experimental measurements of the muzzle vertical deflection for the 
standard rifle with no modifications (A) and the rifle with Recoil Isolator and modified 
receiver ring (B). 


Chapter 4: Barrel Vibration 

You can see in Figure 4-22(A) that the peak acceleration on the unmodified 
standard rifle of about 24 G’s has been reduced to about 4 G’s on the modi- 
fied rifle in Figure 4-22(B). Similarly it can be seen in Figure 4-23 that the 
muzzle vertical velocity has been reduced from 1.9 inches/sec to about 0.3 
inches/sec on the modified rifle. A muzzle vertical velocity of 1 .9 inches/sec 
may not sound like much motion, but we will see later on that it is enough to 
cause the bullet to shoot high by 1.4 inches at 100 yards compared to an 
undisturbed situation. In Figures 4-24(A) and (B) the muzzle vertical deflec- 
tion for the unmodified standard rifle is compared with the modified rifle and 
you can see that the magnitude of the muzzle deflection has been reduced by 
a factor of about six. While a factor of six represents a big reduction in barrel 
vibration, it is considerably less than the factor of twenty or so that we saw in 
the moment data. Well, if you examine the acceleration (Figure 4-22(B)) 
data you can see that most of what we are seeing is high frequency (2.4 kc) 
stuff at a peak amplitude of around 4 G’s and the predominate 1.25 kc third 
mode is not detectable. So, the predominate mode of vibration, which is the 
mode that we are most interested in, has been suppressed by a factor of far 
more than six, just as the moment data indicated. To make it easier for you to 
see this in the data, the periods (i.e., time between peaks) is 0.8 msec for 1 .25 
kc and 0.42 msec for 2.4 kc. Therefore, the accelerometer data is telling us 
the truth and all we are seeing in the data is the high frequency modes that 
were not completely filtered out. The reader is probably getting confused by 
this mode of oscillation discussion, so I have prepared a figure (Figure 4-25) 
that shows physically how a cantilever beam vibrates in the first five modes. 

M F=71 CPS (0.071 Kc) 

i F=445 CPS (0.445 Kc) 

i F=1246 CPS (1.246 Kc) 

M F=2429 CPS (2.429 Kc) 

M F=4036 CPS (4.036 Kc) 

Figure 4-25 - Diagram showing how the barrel vibrates in different modes. 


Rifle Accuracy Facts 

Also, the reader is probably wondering what all this discussion about mode 
of oscillation is about, and whether it has any practical bearing on the prob- 
lem. Well, just have faith, it is important and not just of academic interest. 
What we are seeing in the accelerometer data for the unmodified standard 
rifle (Figure 4-22A)) is the predominate mode 3 with traces of mode 4 and 5. 
In the modified rifle acceleration data (Figure 4- 22(B)) we are seeing prima- 
rily mode 4 with a trace of mode 5, which means that mode 3 has been effec- 
tively eliminated, which has been our objective. The reason for this is that 
we eliminated the forces and moments that are capable of driving the first 
through the third modes, which were relatively slowly varying forces, but did 
not eliminate the forces that drive the higher numbered modes. You see, you 
can’t force a beam to oscillate at frequencies significantly higher than the 
frequency of the driving force. Since the driving moment that we eliminated 
is directly related to the chamber pressure, which has a fundamental fre- 
quency roughly equivalent to mode 3, we should expect the first three modes 
to be excited, but not the higher modes. That means something else is dis- 
turbing the barrel at the higher modes. Well, the way to find out what that 
something else is, is to operate the rifle on the bench without firing a car- 
tridge and make the same measurement. Figure 4-26(B) shows the 

Figure 4-26 - Comparison of the experimental measurement of muzzle acceleration 
on the modified rifle fired with a live cartridge (A) and the muzzle acceleration 
caused by the firing pin impact on an empty cartridge case (B). 


Chapter 4: Barrel Vibration 

acceleration data obtained by simply pulling the trigger with a fired case in 
the chamber of the modified rifle. It looks remarkably like the acceleration 
data on the modified standard rifle fired with a loaded round in Figure 4- 
26(A). This means that the firing pin impact on the primer is driving these 
high frequency modes. An impact force has a very high frequency content 
and is capable of driving the barrel at high frequencies. So, how do we deal 
with the firing pin impact problem? 

Firing Pin Impact 

The only effective way that I know to eliminate firing pin impact is to hang 
your rifle on the wall and don’t shoot it or use electric firing. While I have 
fired primers electrically, there doesn’t appear to be any feasible way to 
apply it to a field rifle. However, ‘not to worry’, because you can prove that 
firing pin impact is not a significant contributor to dispersion. The maximum 
vertical velocity that can result from a 4 G acceleration at a frequency of 
4.2 kc acting over one half cycle (time = 1/4200=0.00024 sec) is 

muzzle vertical velocity = 4x32x12x0.00024 = 0.37 inches/sec. 

where the muzzle vertical velocity is obtained by multiplying the accelera- 
tion in inches/second by the time for a half cycle. Note that on 
Figure 4-23(B) the maximum possible value of the vertical velocity is about 
0.3 inches/sec on the modified rifle, which agrees with our calculation. The 
maximum deflection of the bullet at 100 yards due to a muzzle vertical 
velocity of 0.37 in/sec at an average flight velocity of 3000 ft/sec (time of 
flight=0.1 sec) is 

bullet deflection = 0.37x0.1 = 0.037 inches. 

The dispersion depends on the variation in the firing pin impact force from 
shot-to-shot and according to what I have measured on the bench it may 
amount to as much as 20% to 30%. Therefore, the dispersion resulting from 
variations of firing pin impact force is probably no more than 0.007 to 0.010 
inches (7 to 10 mils at 100 yards). As engineers say, “this is down in the 
mud’’, and not worth worrying about. Some shooters reduce the length of the 
firing pin spring, which reduces the firing pin impact force. Unfortunately, 
reducing firing pin spring stiffness also reduces reliability and increases the 


Rifle Accuracy Facts 

time of fall (e.g., lock time), which is already 2.4 msec on this rifle. Increas- 
ing the firing pin time of fall gives the rifle more time to move between the 
time the trigger is pulled and the bullet exits the muzzle, consequently, accu- 
racy can only suffer. Other shooters try to reduce the lock time by increasing 
the stiffness of the spring, but this will increase barrel vibration and can make 
the bolt difficult to operate. Brownells sells a Tubb titanium firing pin that is 
half the weight and a spring that has a 16% increase in stiffness. This combi- 
nation decreases the lock time by 35% while maintaining the impact energy 
roughly equivalent to the standard firing pin assembly. So, with this set up, 
the firing pin disturbance is the same, but the lock time is reduced. This 
modification may help accuracy particularly when firing from standing or 
sitting positions, so it may be an improvement on target rifles. Since I don’t 
know of any simple way to evaluate the effect of lock time on accuracy, I am 
inclined to leave the firing pin design alone, because there is no clear 
evidence that making a change will reduce dispersion. 

Cartridge Case Wall Thickness Asymmetry 

If the cartridge case wall thickness varies around the circumference of the 
case, there will be a thick side and a thin side. When the case is pressurized 
the thin side should stretch more than the thick side in the axial direction. 
This should shift the bolt thrust slightly off the center line of the action, and 
cause a moment. The moment will, of course, make the barrel move and 
produce dispersion. There has been quite a bit of discussion of this problem 
in bench rest publications (i.e., “Precision Shooting”). I modified a Forster 
Coax Gage, as suggested by Olsen in the March 1993 issue of “Precision 
Shooting”, to measure case wall thickness. After running a bunch of 
Remington cases through this gadget the results were as follows. 

Percent of Cases Wall Thickness Difference 

35 <0.001 

15 0.001 to 0.0015 

30 0.0015 to 0.0025 

20 0.0025 to 0.004 

The results show that about half the cases are pretty good, but about half 
show wall thickness differences of 2-4 mils. Now, 4 mils is about a 16% 
difference in side-to-side thickness, and that could make a significant 


Chapter 4: Barrel Vibration 

difference in bullet impact. I made a rough theoretical calculation that indi- 
cated one might expect as much as 0.25 inches dispersion from this source. 
The only way that I know to test this effect is to take a bunch of the worst 
cases, and index five rounds with the thin side up and five rounds with the 
thin side down. If there is an effect, there should be two groups displaced in 
the vertical direction. Well, I tried this and the results were inconclusive. In 
retrospect, I decided that one might not expect to see an effect where one has 
a normal headspace (0.002 inches) combined with a chamber that has moder- 
ately rough walls and a spring loaded ejector that pushes the case all the way 
forward. You might see this effect in a bench rest gun where the chambers 
are highly polished and there is usually no spring loaded ejector combined 
with minimum headspace. In my experiment the case probably stuck to the 
sides of the chamber so that no effect was seen. 

We now turn to the computer to determine how much dispersion we can get 
from barrel vibration. 

Barrel Vibration Computer Simulation 

A computer code was developed that accurately predicts the vibratory mo- 
tion of a rifle barrel. Since the average reader will not be interested in a lot of 
detail on this code, only a brief description will be given. If more detail is 
needed, the reader can turn to Appendix B where a somewhat detailed dis- 
cussion is given. The computer code is not reproduced because it is very user 
unfriendly. The barrel is divided into 24 elements, where the motion of each 
element can be described by an equation. The equations contain influence 
coefficients which calculate the influence of all the other elements on a single 
element. In this way the forces and accelerations acting on an individual 
element can be calculated and also the motion of the individual elements can 
be calculated. The code was checked by comparing the acceleration data 
obtained on a vibrating cylindrical beam, which verified the code. 

Figure 4-27 shows a sketch of the barrel that indicates the individual ele- 
ments and the circular symbols show how the barrel droops downward as a 
result of gravity. It may surprise you to find out that the barrel droops about 
5.3 mils as a result of the action of gravity. Figure 4-28 shows the barrel 
deflection for progressive time steps with the gravity droo p removed for clar- 
ity, and you can see that a wave forms that propagates toward the muzzle. 


Rifle Accuracy Facts 

^ RECLiyLK^ 

•- ' 

§ * 

P m 

jjjj g 0< 

^ -5 

* * * 0 * *"*"• "® • # n 

® ® ♦ © # 

® ® «, 

® ® ® 

— * ♦ • • 

Figure 4-27 - Computer drawing showing how the barrel is divided into elements for 
calculation of barrel vibration by the barrel vibration computer code. It also shows 
how gravity causes the barrel to droop. 

Figure 4-28 - Computer drawing showing how the barrel vibrates as predicted by 
the barrel vibration computer code for various selected times. The gravity droop 

has been removed for clarity. The bullet symbol indicates the position of the bullet 
in the barrel. 

The scale indicates a deflection of 2.5 mils and the scale is greatly exagger- 
ated for clarity, so you can see that the barrel does not move very much. 
However, it is enough to cause considerable dispersion. Note that if you 
compare the wave shape of the distorted barrel it agrees very well with the 
third mode of oscillation shown in Figure 4-25. The miss distance, which is 
the difference in point of bullet impact between this case with vibration and 
the point of impact of the undisturbed barrel, is 1 .406 inches. The barrel 


Chapter 4: Barrel Vibration 

vibration computer simulation tells us that the muzzle end of the barrel is 
pointed upward with an angle of 0.0175 degrees and the muzzle is moving 
upward at a velocity of 3.08 inches/sec when the bullet exits. The vertical 
velocity accounts for about 0.3 inches of miss distance and the muzzle angle 
accounts for about 1 . 1 inches of the total miss distance. Now, if the moment, 
and consequently the muzzle motion was the same with every shot, this change 
in impact point would not cause any dispersion. But, the moment can vary 
by about ±30% from shot to shot and this means we get about 60% of this 
change in impact point, or about 0.8 inches of dispersion. The variation in 
moment is primarily caused by variations in bolt thrust plus the other factors 
that have been discussed. This estimate of the variation of moment, and in 
effect the amount of vibration, is based on the analysis of roughly 800 oscil- 
loscope records taken on the unmodified standard rifle. Obviously, that is a 
lot of data, so the estimate of the variation should be reasonably good. But, 
just how good is this computer simulation of barrel motion? Well, it’s pretty 
good, as you can see in Figures 4-29, 4-30, 4-31, and 4-32, which compare 
the nominal experimental and theoretical values for receiver moment, 
muzzle acceleration, muzzle velocity, and muzzle deflection for the unmodi- 
fied standard rifle, all in the vertical plane. 


l/l 500 


O 400 



O 300 




2 100 



1 1 , 









m 0< 


^ -i00 




a 0 

.2 0.4 0.6 0.8 1.0 1.2 1.4 


Figure 4-29 - Comparison of the measured experimental receiver ring moment for 
the unmodified standard rifle in the vertical plane with the calculated moment from 
the barrel vibration computer codes. 


Rifle Accuracy Facts 

0 .2 .4 .6 .8 1.0 1.2 1.4 


Figure 4-30 - Comparison of the measured experimental muzzle vertical accelera- 
tion for the unmodified standard rifle with the muzzle acceleration obtained from the 
barrel vibration computer code. 














0 .2 .4 .6 .8 1.0 1.2 1.4 


Figure 4-31 - Comparison of the measured experimental muzzle vertical velocity for 
the unmodified standard rifle to the calculated muzzle vertical velocity from the 
barrel vibration computer code. 

Before leaving the theoretical work, we need to point out that the strain gages 
actually measure what is known as the response moment, which results from 
an actual applied moment. You see, the moment we measured is much smaller 
than the real moment that was applied by the recoil lug and asymmetric 


Chapter 4: Barrel Vibration 

Figure 4-32 - Comparison of the measured experimental muzzle vertical deflection 
for the unmodified standard rifle to the calculated muzzle vertical deflection from 
the barrel vibration computer code. 

receiver. The reason for this is that the barrel just can’t respond quickly 
enough, so that the response moment would equal the applied moment. Both 
the applied moment, which peaks at about 1500 inch-pounds, and the re- 
sponse or measured moment, which peaks at about 450 inch-pounds, are shown 
in Figure 4-33. The reason for discussing this is to point out that the true 
moment (applied moment) that is actually forcing the barrel to move is very 
large, about three times the measured or response moment. Also I need to 

Figure 4-33 - 
Calculated applied 
and response 
receiver ring moment 
for the unmodified 
rifle showing how the 
actual applied 
moment is much 
larger than the 
response moment. 
The response 
moment is the 
average moment 
measured by the 
strain gages. 


Rifle Accuracy Facts 

point out that the stiffening effect of internal pressure was found to be negli- 
gible. A barrel is a thick walled cylinder compared to a fire hose for example 
and the effect is insignificant (Reference 17). In addition, the fact that barrel 
gravity droop causes the bullet to travel a curved trajectory in the bore that 
generates an upward centrifugal force on the barrel was evaluated and 
found negligible. 

Horizontal Dispersion 

We now need to consider the effects of muzzle motion in the horizontal plane. 
While I did not make nearly as many measurements in the horizontal plane 
as I did in the vertical plane, I made enough to convince me that the horizon- 
tal motion of the muzzle is about 1/3 of that in the vertical plane (0.8 inch). 
Thus, the unmodified standard rifle dispersion in the horizontal plane should 
be about 0.27 inches. This would make sense, because the only obvious 
asymmetry in the horizontal plane is the vent hole (1/8 inch diameter) drilled 
in the right side of the forward receiver ring. This hole is supposed to vent 
gas escaping through a hole in the bolt head. I doubt that this vent hole really 
works, because the hole in the bolt head opens into the bolt lug raceway, and 
most of the escaping gas would flow through the raceway and out the loading 
port. In a new action design I would leave it out. Anyway, this asymmetry 
was eliminated by drilling a matching hole on the opposite side of the ring. 

The reader should be warned that drilling holes in a rifle forward receiver 
ring may be dangerous. While a stress analysis indicates that the receiver 
ring still has a very large factor of safety with the two additional holes, you 
simply cannot be sure that the procedure is safe without testing to destruc- 
tion. Such testing has not been done. 

I believe that we have evaluated the barrel vibration problem with a high 
degree of certainty, and I also believe that we have eliminated the significant 
causes of the vibration. The next step is to test fire the modified rifle for 
group size and see if there is any improvement. 


Chapter 4: Barrel Vibration 

Accuracy Test 

The results of the accuracy firing tests on the modified rifle with the new 
barrel are shown in Table 4. The tests were performed using a standard bench 
rest firing setup, and the results are a summary of twenty 5 shot groups. The 
group sizes are measured with a dial gage micrometer, and represent the 
extreme or largest spread between centers of the bullet holes. 



Accuracy Test (5 shot groups at 100 yards) 

Average Maximum Minimum 

0.884 1.223 0.408 

Now, you may have expected better results, but remember that this rifle typi- 
cally would shoot 1.5 inch average groups before we started the modifica- 
tions. Consequently, we have improved the accuracy by nearly a factor of 
two, and that is real progress. Also, there are several more known errors in 
the rifle that can account for the remaining dispersion. 

Accuracy Testing 

We need to talk about the statistics involved in testing. Most people think that 
if you have a ballistic system (i.e., rifle) that has two error sources and you 
eliminate one of the errors, the resulting dispersion will be reduced by the 
amount of the eliminated error. Unfortunately, it doesn’t work that way, and 
depending on the number of error sources in the system, the resulting disper- 
sion will usually be reduced by a much smaller amount. The reason for this 
is that the total dispersion of a system is equal to the square root of the sum of 
the squares of the individual error sources. 

Total Error = V(A 2 + B 2 + C 2 + D 2 + •••) 

where A, B, C, and D are the individual error sources. 


Rifle Accuracy Facts 


Figure 4-34 - A plot of dispersion as a function of the number of error sources 
remaining in the rifle where there are initially six equal errors of 0.6 inches. This 
demonstrates the difficulty in determining when an error source has been 
corrected by test firing. 

Figure 4-34 shows how the calculated dispersion for a rifle with six equal 
sources of error (i.e., 0.6 inches) changes as you gradually remove each source 
of error. Note that when the first 0.6 inch error is removed, the dispersion 
improves from 1 .47 inches to 1 .34 inches and not from 1 .47 to 0.87 inches as 
many people might expect. In other words, as long as any other significant 
sources of error remain in a rifle you usually can’t detect the full effect of 
eliminating a single error. One of the best examples of this effect that I have 
seen happened at least twenty years ago. A very reputable ballistics labora- 
tory was given a contract to determine the effect of bullet tip mutilation on 
group size. The firing tests were run using a Mann barrel, which is a large 
diameter (about 3 inches) barrel mounted on a concrete pylon. This configu- 
ration should eliminate sighting and barrel vibration errors, however, at least 
two other significant errors remained, which we will investigate in later chap- 
ters. Well it turned out that the average group sizes were around 0.6 inches, 
and no effect was detected. It turns out that mutilation of bullet tips does 
have a small effect that can only be calculated (Chapter 10), but this effect 
was obscured by the other remaining error sources. All that this test 
established was that the error was significantly less than the group size, which 


Chapter 4: Barrel Vibration 

is something that professional ballistics people already knew. The point of 
all this is not to expect the group size to be improved by the full amount of 
error that was attributed to barrel vibration (0.84 inches), because there are 
still some other significant errors present. The other point to be made is that 
it may be difficult to tell whether or not you have eliminated a source of 
inaccuracy by test firing. 

When I started testing this rifle I had expected to get approximately a 0.65 
inch average group. When the average group sizes turned out to be signifi- 
cantly larger (i.e. 0.94), I decided to check the throat by making a sulphur 
cast of the throat. This barrel had been fired between two and three thousand 
times, and I was suspicious. Sure enough, the cast showed that the rifling in 
the throat had eroded forward by about 0.43 inches. That is considerably 
more than I would have expected, and too much to be corrected by setting 
back the barrel. Consequently, the only thing to do is to start over with a new 
barrel. The new barrel was made from a new Douglas blank and was cham- 
bered with the same tools used on the original, so it should have been as near 
identical as two barrels could be. This barrel was used in obtaining the 
results shown in Table 4. 

Action Bedding 

There has been a lot written about epoxy bedding and most of it consists of 
unsubstantiated claims. Contrary to all the grandiose claims, I can’t see a big 
difference in sporter accuracy between a good inletting job and epoxy bed- 
ding. However, it may make a small difference in the case of a sloppy factory 
bedding job. Since it won’t hurt anything, and may make you think you have 
done something good, you might as well epoxy bed the action if you feel like 
it. I have found a thin coat of plain old Elmers epoxy to be as good as any- 
thing. I don’t like glass filled epoxy because it wrecks sharp chisels and I 
don’t think it is any better. The strongest epoxy for bedding is aluminum 
filled Devcon F which has a putty consistency and is easier on chisels. How- 
ever, it may show as a bright line around the edges of the inletting. This stuff 
is noticeably stronger than ordinary epoxy, if that is important. Epoxy bed- 
ding will protect the wood from deterioration from oil soaking and should 
cause the action to come closer to assuming the same position in the stock 
after each shot. But like I say, I can’t really tell any difference. 


Rifle Accuracy Facts 

Figure 4-35 - Cross-section view of the stock forearm tip showing how cardboard 
shims coated with epoxy are placed in the barrel channel in O’Connor bedding 
approach. A differential force of 10-20 pounds is required. Barrel vibration is 
reduced by a factor of two over a free floating barrel. 

Figure 4-36 - 
Measured forward 
receiver ring moment 
with O’Connor 
bedding showing how 
the moment is 
reduced by about 
50% compared to a 
standard rifle. See 
Figure 4-3 for 


Chapter 4: Barrel Vibration 

The only conventional bedding method that I have found that definitely im- 
proves accuracy is what I call the O’Connor method. I call it the O’Connor 
method because I think I first read about it in O’Connor’s column some 50 
years ago. Whether it was his idea or the idea of a gunsmith of his 
acquaintance, I can’t say. But it works well enough to improve the accuracy 
of most commercial rifles by about 20 to 30 percent. The idea is to bed the 
action so that the forearm tip of the stock contacts the barrel with an upward 
force of 10 to 20 pounds. The barrel should be free of the stock from the 
action to the tip of the forearm. It may be necessary to remove some of the 
wood from under the front of the receiver to tip the barrel down enough to 
achieve the 10-20 pound load. It is best to place two epoxy coated inserts 
(i.e., see Figure 4-35) in the barrel channel spaced circumferentially by about 
120 degrees and the receiver should be epoxy bedded. This method helps 
because it applies a preload moment, which is a method commonly used by 
design engineers. Figure 4-36 shows the forward receiver ring moment 
measured on the standard sporter rifle with O’Connor style bedding. If you 
compare Figure 4-36 with Figure 4-3, you can see that the recoil moment has 
been reduced by nearly 50%, which is a significant amount. Notice also that 
the amplitude of the high frequency oscillations has been reduced, probably 
as a result of the friction damping between the forearm and the barrel. The 
point of impact may drift downward slowly for several months after the ac- 
tion is bedded in this manner but it will eventually stabilize. A violent change 
in weather conditions, particularly humidity, could cause a shift in point of 
impact. However, I have carried hunting rifles from the Mexican border to 
the northern Yukon Territory for years that were bedded in this manner and 
never had any trouble. I think most of the trouble with shifting point of 
impact comes from using improperly seasoned and aged stock wood. A stock 
blank should be aged for at least five years before it is used so that it has time 
to stress relieve. There is a commercial device (AccuMajic Accurizer) made 
by Aftermarket Innovations (1-800-528-6900) that seems to accomplish the 
same thing as O’Connor bedding. I have not tested this device but according 
to an article in the February 1996 Shooter’s News (1-216-979-5258) it seems 
to work the same way. Anyway, we now have experimental data showing 
why O’Connor’s method works and I can recommend it for hunting rifles. 

Pillar bedding has been used in bench rest rifles with free floating barrels. In 
this type of bedding two 1/2 to 5/8 inch diameter aluminum rods with holes 
for the guard screws are epoxy bonded in the stock. The upper surface of the 


Rifle Accuracy Facts 

pillars are machined to fit the bottom surface of the receiver. This type of 
bedding holds the receiver in the stock very rigidly, and apparently reduces 
flexing of the action. I tried this about 30 years ago and found that it does 
help with a free floating barrel. I don’t like it on a hunting rifle because it 
makes the action noisy. These days most bench rest rifles have the actions 
glued in a plastic stock which is very successful. 

Barrel Weight 

Everybody seems to think that increasing barrel weight improves group size. 
The question is just how much? Calculations were made with the barrel vi- 
bration code for a 1 .2 inch constant diameter barrel, which weighs 7.5 pounds. 
The usual light barrel weighs between 2.7 and 3 pounds. The barrel in the 
experimental rifle weighs 2.8 pounds. The results indicated that the disper- 
sion error due to vibration would be reduced by roughly a factor of four. 
Consequently, reducing barrel vibration by increasing barrel weight results 
in a large weight penalty, although it does work. I once made one of these 
monsters using a heavy handmade version of the 721 action, and it did shoot 
well. However, it didn’t shoot much better than our experimental rifle modi- 
fied to eliminate barrel vibration effects. One of the biggest improvements 
with a heavy barrel is that it is easier to shoot accurately, because it doesn’t 
move around as much as a result of its increased inertia. Someone may won- 
der if the barrel vibration code could be used to optimize the contour of a 
light barrel. Well it probably could be used for that purpose, but it would 
have to be used in a trial and error approach, which is difficult to do. I would 
prefer to eliminate the vibration in the first place, just as we have done. If the 
barrel vibration is eliminated, barrel weight is no longer an important consid- 
eration in a sporter. 

While making barrel vibration calculations I decided to try to determine the 
most important parameter in a barrel-stiffness or weight? The neat thing 
about a computer simulation is that you can change both material stiffness 
and density in a completely arbitrary way and see what happens. In fact in 
some cases that I ran, the gun would have had to be made of “Unobtainium”! 
Well, the upshot of all this is that a heavy, flexible barrel is the best. I think 
this will shock most target shooters, because I’m always reading articles that 
tell you how to optimize the stiffness in a barrel. People have even milled 
longitudinal slots in the barrel in an attempt to reduce weight while maintaining 


Chapter 4: Barrel Vibration 

stiffness, which is just the opposite to what the computer simulation is telling 
us. Most of the experts seem to think that fluting doesn’t help. Well, if you 
stop and think about it, if you had a heavy barrel that was hinged at the action 
so that the torques generated in the forward receiver ring could not be trans- 
mitted to the barrel, the barrel wouldn’t move much. Unfortunately, this is an 
impractical solution, so we have to compromise. A possible compromise is 
to use a light sporter steel barrel, that is as flexible as you can get, and add an 
overcoat of lead that more than doubles the barrel weight without signifi- 
cantly increasing the stiffness. I tried the lead coating once to see if I could 
make it work. The muzzle diameter was 0.97 inches at a barrel length of 24 
inches, which meets the bench rest rules. It did not work because the lead 
sleeve came loose. Of course, this is not a useful solution in the case of a 
sporter, but could be useful in the case of a bench rest rifle if one could get it 
to work. The sleeve might stay put if the barrel were given a rough finish. 

Muzzle Weights 

Weights have been attached to the muzzles of rifles in an attempt to improve 
accuracy, and under the right conditions they probably work. One indication 
that they may be effective is that according to the literature, the addition of 
recoil compensators to the muzzle improves accuracy. I have had no first- 
hand experience with recoil compensators, so I don’t know whether or not 
this is true. The barrel vibration computer code was used to compute the 
effect of muzzle weight on dispersion, and you can see in Figure 4-37 that 
the addition of 0. 1 8 pounds to the muzzle reduces dispersion due to vibration 
by about a factor of 2 on the unmodified, standard rifle. This is a large im- 
provement for such a small weight penalty. One thing that I am sure of with 

Figure 4-37 - Calcu- 
lated effect of a 
muzzle weight on the 
miss distance due to 
reduction in barrel 
vibration. A small 
muzzle weight 
theoretically reduces 
barrel vibration 



Rifle Accuracy Facts 

regard to muzzle weights is that they must be rigidly attached. Otherwise, 
they can cause large dispersion. Silver solder seems to be the only reliable 
method. Unfortunately, I don’t know any good way to test a muzzle weight 
to make sure it is really working. Later, when we have eliminated the other 
errors that are still present in the rifle there shouldn’t be any difference, be- 
cause most of the barrel vibration should have been removed by the action 
modifications and the Recoil Isolator. Therefore, we may be able to check 
again to see how efficient the modifications have been. 

Theoretically, a tuned mass damper, which is a spring mass gadget that if 
tuned properly, could be used to damp muzzle vibration. The problem with 
using a mass damper is that it will only damp a single frequency and we have 
several modes present in barrel vibration. So, it gets tricky to apply them. 
They have been successfully used to damp tall buildings and rotating 
machinery where the vibration consists primarily of a single frequency. I 
have tried mass dampers in computer simulations where we have a single 
third mode and it works, but I don’t know how well it would work in practice. 

Other Actions 

Earlier, it was stated that the Remington 721 was chosen primarily because it 
has a cylindrical receiver, which makes strain gage instrumentation easier. 
Many actions, such as the 98 Mauser, Winchester Mod 70, and others, have a 
flat projection on the bottom of the receiver, which will greatly complicate 
the strain gage measurement of moment on the forward receiver ring. In fact, 
I am not sure that such a measurement can be made with any confidence. 
The other thing about these unsymmetrical receivers is that they would be 
difficult to modify in order to improve symmetry. The question arises as to 
whether or not barrel vibration is worse on this type of action as a result of 
the asymmetry. Since I haven’t made measurements on this type of action, I 
can only guess that barrel vibration would be worse for the same barrel weight 
and receiver ring thickness. However, most rifles with this style of action 
seem to have heavier barrels and larger diameter receiver rings. Consequently, 
it is possible that these differences compensate, at least to some extent for the 
asymmetry, by adding the extra stiffness and weight. This could be 
investigated by measuring acceleration on the muzzle. However, I don’t in- 
tend to pursue this matter, because in view of the results already obtained, the 
flat bottom receiver appears to be a poor design. 


Chapter 4: Barrel Vibration 

Throat Erosion 

Let’s take time out to talk about throat erosion, since we have inadvertently 
stumbled into it. Throat erosion is caused by three known mechanisms. 

1 ) ablation - Shear stresses developed in the moving gas layers next to the 
bore surface tear away steel particles. 

2) chemical erosion - Oxygen molecules and ions chemically combine with 
iron molecules on the surface of the bore to form iron oxides, which are 
weak and easily torn away. This process is similar to oxy-acetylene gas 
cutting and increases with temperature. 

3) mechanical erosion - Graphite, primer grit, and unburned carbon 
particles strike the bore surface mechanically removing steel particles. 
The bullet jacket scrapes molecules off the surface of the throat. 

All of these mechanisms contribute to throat erosion, and a lot of effort has 
gone into improving powder and barrel steel to reduce the effect. However, it 
is not clear which one is the most damaging. Forced to make a choice, I 
would pick chemical erosion as much the worst of the three. It is clear that 
high pressures and high temperatures increase erosion, and this would be 
true of all three mechanisms. Also, the larger the case capacity, relative to 
the bore area, the faster erosion occurs. In fact, cartridges like the 220 Swift 
and the magnums often will burn out a throat in one to two thousand rounds. 
However, the 270 Winchester is a standard cartridge and should last at least 
3,000 rounds under normal conditions. I think the early and drastic throat 
erosion in this situation resulted from firing under unusually high tempera- 
ture conditions. I often fired 40 rounds fairly rapidly without cooling when 
taking data for this chapter. When all the electronics were working properly, 
I worked as fast as I could to get the data. Since the ambient temperature was 
often in the 90’s, the barrel became very hot. 

The only solution to the problem is to keep the barrel reasonably cool. I 
normally pour water down the bore through a 1 .5 foot long 3/8 inch diameter 
copper tube which has a plastic funnel attached to the tube with rubber goop, 
after each two or three five shot groups. This couldn’t be done with the 
instrumented rifle mounted on the machine rest. I don’t know whether or not 
the use of IMR483 1 powder contributed to the rapid throat erosion, but it 
does seem to leave more powder residue in the bore than other powders. 


Rifle Accuracy Facts 

Anyhow, I was surprised to see so much erosion occur in two or three thou- 
sand rounds, and while there is no way to prove it, high temperatures were 
probably the cause. 

Figure 4-38 - Photograph of rail gun used in testing. See Appendix F for 
complete description. 

Special Bench Rest Gun Problem 

Later on during research on muzzle blast effects, I switched from a sporter to 
a rail gun (Figure 4-38 and Appendix F) and to 6mm cartridges. The switch 
to 6mm cartridges was made so that I could use bench rest match bullets 
which are much better than ordinary commercial bullets. I also built a 
Tunnel Range (Appendix E) with the help of the Zia Rifle Club to eliminate 
wind effects. The goal was to eliminate all dispersion errors not associated 
with ammunition defects and was successful. In the process of modifying 
the rail gun so that it was as free of barrel vibration as I could make it, I 
measured the moment on the barrel near the barrel block mounts and found a 
very low amplitude oscillation at 4-5 kc and 9-10 kc. At the time I didn’t 
think these very low amplitude high frequency oscillations could cause a 
problem, but it turned out that they did. 


Chapter 4: Barrel Vibration 

The rail gun has a 1.350 inch diameter cylindrical barrel clamped to the car- 
riage with solid aluminum blocks, and the muzzle only extends 18 inches 
beyond the barrel blocks. The carriage, which weighs 45 pounds slides to 
the rear during recoil on low friction Teflon bearings. This is a very rigid 
system and as a consequence the barrel vibration frequencies are much higher 
than a sporter. When I fired groups with different powder loads I noticed that 
the point of impact changed more than one would expect from differences in 
gravity drop. So, I fired 3 or 4 five shot groups at each powder load varying 
from 26 to 30 grains at half grain intervals and measured the average center 
of impact with respect to a single reference. The muzzle velocity was also 
measured. Since this gun averages about 0.180 group sizes the accuracy of 
the vertical group center measurements is fairly good (±0.020 inch). The 
data were corrected for the varying gravity drop due to varying velocity and 
plotted in Figure 4-39 compared to a 9.5 kc sine wave. The sine wave is, in 
effect a representation of the vertical velocity of the muzzle (divided by 10) 
when the bullet exits. The peaks in the data indicate the maximum deflection 
in the vertical direction either upward or downward from the mean. Since 
the flight time at 1 00 yards is approximately 0. 1 second, one can obtain the 
vertical velocity by dividing the peak value by 0. 1 . Of course the result is 1.2 
inches per second. Now the importance of knowing this is that one can choose 
a powder load or muzzle velocity that is optimum for reducing this error. 
Note that if you operate on the peaks (i.e., 26, 27, 28, 29.2 grains) you can 

Figure 4-39 - Plot 
showing variation of 
vertical position of rail 
gun center of group 
impacts at 100 yards at 
different powder loads 
and muzzle velocities 
compared with a 9.5 Kc 
sine wave. The 9.5 Kc 
frequency was observed 
in barrel vibration 
measurements. The 
impact points were 
corrected for differences 
in gravity drop. 


Rifle Accuracy Facts 

u, °- 4 l 








>- a; 



— i 

;un - 

6BR - 


H322 - 

- 68 G 






i 8 


| 2 

n % 



i 3 


» 6 u 

• 4 < 

» ,£ 

► 6 



► 3 < 

■ —*■' 1 

1 V, 







2 ? 20 29 



Figure 4-40 - Graph 
showing 5 shot 
group size from the 
rail gun in the Tunnel 
Range with different 
powder loads. 

have a muzzle velocity extreme spread of 40 fps (equivalent to ± 0.2 grains) 
without having a large variation in impact due to this effect. On the other 
hand operating at the crossover points (i.e., 26.5, 27.5, 28.5, 30 grains) where 
the slope is steep you would expect to see a vertical error contribution of 0. 1 6 
inches due to variation in muzzle velocity of ± 20 fps. While the group size 
data (Figure 4-40) only roughly correlate with Figure 4-39, the best results 
seem to be at a load of 27 grains of H322 powder. This group averaged in the 
high one’s (i.e., around 0.18 inches). The worst group averages were in the 
mid two’s (i.e., around 0.30 inches) at 29 grains. The loads below 27 grains 
are too light for consistent muzzle velocities. 

We found a similar variation in the vertical position of groups with a heavy 
varmint 6PPC bench rest gun belonging to a friend (Dr. Jackson). Figure 4-41 
shows a plot of the vertical variation of point of impact with gravity variation 
removed for this gun. Notice that the frequency is lower as one might 
expect — about 6.7 kc instead of 9.5 kc. But it appears to be the same 
phenomenon. The vertical stringing of the group size (not shown) is at a 
minimum below 3100 fps and above 3300 fps. This correlates with the 
negative slope of the sine wave, and I believe this is to be expected. If the 
muzzle velocity is higher than the mean for the group it would have a little 
less gravity drop and normally would impact a little higher. But, if the gun is 
operating on the negative slope the higher shot will be corrected downward 
to the group center by this high frequency vibration phenomenon. The best 
place to shoot is just past a positive peak on the curve. We have found that 


Chapter 4: Barrel Vibration 

Figure 4-41 - Plot 
of the vertical 
positions of group 
centers for 
various muzzle 
velocities on a 
6PPC benchrest 
rifle. The effect of 
varying gravity 
drop due to 
differences in 
velocity has been 

the amplitude of the sine curve is less (about half) with the free recoil method 
of shooting than it is with the firm hold method. This is not surprising, since 
some of the shooters body weight is effectively transmitted to the stock in the 
firm hold approach. This increases barrel vibration amplitude. In the free 
hold only the trigger is touched by the shooter. Of course, you can’t use the 
free recoil method with light sporters or heavy recoiling guns. Consequently, 
this only applies to heavy bench rest guns. 

I decided to test my bench gun which is the completely modified action in- 
cluding the Recoil Isolator with a heavy varmint Shilen barrel chambered in 
6mm BR. The data are shown in Figure 4-42. You can see that when the data 
are corrected for the variation in gravity drop it becomes essentially a hori- 
zontal straight line. This shows that there is very little barrel vibration in- 
volved in this gun, otherwise we would see a sine wave variation in group 
center of impacts in the vertical plane just like we saw in the rail gun and the 
custom heavy varmint gun. 

While this is not a problem with sporters, it could be a problem with bench 
rest guns where shooters try to shoot groups that average less than 0.2 inches 
at 100 yards. Vertical stringing of groups is common in bench rest guns and 
the typical approach is to keep increasing the load until it stops. Unfortu- 
nately, this won’t always work because you run into the maximum pressure 
restriction or the vertical dispersion may be caused by another problem. 
Vertical stringing of groups can be caused by bolt lugs not seating evenly on 


Rifle Accuracy Facts 

Figure 4-42 - Plot 
of the vertical 
positions of 5 shot 
group centers for 
various loads and 
muzzle velocities 
in the modified 
721 action with 
recoil isolator and 
heavy varmint 
6mm BR barrel. 
Gravity drop 
variation is 

the receiver lugs. In a rail gun this bolt lug problem is eliminated. With a rail 
gun you can change the vibration frequency by moving the barrel either for- 
ward or backward in the barrel blocks, which changes the phase of the oscil- 
lation. This may allow one to find a reasonable load that minimizes vertical 
dispersion. With a bag gun (i.e., bench rest gun fired from sand bag rests) 
one might reduce the length of the barrel to obtain an optimum result, al- 
though I would check the top and bottom bolt lugs for equal bearing first. I 
would also be suspicious of the threaded barrel joint in a bench rest gun 
(See Chapter 6). 

Once you have established the best velocity for accuracy you should test 
every new bottle of powder to make sure that you are getting the same veloc- 
ity for a given load. We have found that different bottles of powder with the 
same lot number sometimes have different characteristics. 


Chapter 4: Barrel Vibration 


We have at this point measured the moments on the forward receiver ring and 
evaluated their effect on accuracy. We have also eliminated the recoil mo- 
ment through the use of a special bedding device called a Recoil Isolator, 
which does not transmit the recoil force from the stock to the receiver until 
the bullet has left the barrel. This eliminates the recoil moment effect on the 
receiver that contributes to barrel vibration and inaccuracy. We also found 
that the receiver structural asymmetries were another source of moment and 
made modifications to the receiver to eliminate these sources of vibration. 
The motion of the muzzle of the barrel was measured with an accelerometer, 
and these data proved that we had greatly reduced barrel vibration. 

A barrel vibration computer simulation code was used to estimate the contri- 
bution of barrel vibration to the dispersion of the rifle, and found it to be 
about 0.84 inches on the standard unmodified rifle. Accuracy tests were run 
with five shot groups at 1 00 yards, which show that the normal average group 
size of 1.5 inches on a standard rifle was reduced to 0.884 by the modifica- 
tions that were made. 

We also demonstrated that barrel vibration causes a vertical shifting of the 
center of impact of groups with changing muzzle velocity. 

Now that we have effectively eliminated barrel vibration, there are at least 
six more significant errors remaining in the rifle that have to be corrected. 
They are scope sight motion, barrel joint motion, muzzle blast effects, bullet 
core problems, bullet imbalance, and external ballistics problems. We work 
on scope sight problems in the next chapter. 

Congratulations! You have just made it through the most difficult part of 
the book. I promise that there will be no more electronics and other stuff that 
makes for difficult reading. 


Rifle Accuracy Facts 


S cope sights and their mounts have mechanical problems that can cause 
dispersion, so we will take care of this before we get into some of the 
more complicated and less obvious problems. These mechanical problems 
generally fall into two categories, motion of the optics and motion 
of the mounts. 

Optical Parts Motion 

A number of years ago I bought two expensive high-power variable scopes 
of a well known brand that were identical. I noticed that my shooting accu- 
racy suddenly deteriorated, and decided something had to be wrong with the 
scopes. The only thing to do was to mount the receiver in a rigid vise then jar 
the mounted scope and see if the reticule returned to the same aiming spot. 
Well you guessed it. Every time I gently tapped either one of these scopes, 
the reticule returned to a different spot! I repeated the experiment with an- 
other scope of different manufacture and the reticule always returned to the 
same spot. There was just no doubt about it, some of the optics inside the 
scope were not rigidly mounted. The problem turned out to be in the way the 
objective lens (i.e. front lens) cell was mounted in the parallax adjustment 
mechanism. Well, I fixed one of these scopes by modifying the objective 
lens cell mount and traded the other one off for another scope. I won’t 


Rifle Accuracy Facts 

mention the brand that was unsatisfactory, because it happened too many 
years ago and they may be perfectly satisfactory by now. This experience 
taught me that scopes can be faulty, and the only way to tell is to bench test 
them. When you run a test like this you should use a heavy, rigidly mounted 
vise with lead lined jaws. I use a small, light piece of softwood to tap the 
scope, and you need to tap the scope in several places and at different angles. 
It doesn’t take much of a blow to make the reticule jump, and you don’t want 
to hit the scope tube too hard or you might dent it. So far, I have not had 
trouble with Weaver, the old Leupold 20X, or Bausch and Lomb. Recently I 
have had trouble with a new 24X target scope, and after making several tele- 
phone calls I found that everybody in the bench rest fraternity was having the 
same problem. A few people have started small businesses rebuilding some 
target scopes. Now to put this in the proper perspective I have to tell you that 
the recoil acceleration is much higher than normal on our experimental rifle, 
as the following table shows. 



Table 5 - Peak Recoil Acceleration 






Experimental 270 



Standard 270 Sporter 



Light Varmint, 6PPC, 6BR 



Heavy Varmint, 6PPC, 6BR 



Well, you can see that a scope gets a very severe ride on the experimental 
rifle because the recoil isolator causes the recoil weight to be lower than 
other rifles with the same total weight. 


Chapter 5: Scope Sight Problems 

Also, note that the acceleration is much lower on typical bench rest rifles. 
This means that a particular target scope may be all right on a heavier rifle, 
without the recoil isolator. 

There is one way around this problem that may eventually work, and that is 
to use a spring loaded sliding scope mount, similar to the old Unertl mount. I 
tried an old Unertl scope and mount, but it was never designed to take these 
heavy loads and did not work. I then tried designing a mount using a similar 
approach, but it also failed. In retrospect, this mount had several design flaws 
and could not have performed properly. However, I believe that the sliding 
mount approach could be used to successfully reduce the recoil acceleration, 
but it will take a lot of work. 

This scope optics movement problem is very insidious, because it is difficult 
to detect. If I hadn’t been shooting a very accurate rifle, I might never have 
noticed that the scopes were defective. The only way to find out is to test by 
both bench testing and firing. In spite of everything you do I don’t know of 
any way of being absolutely certain that the scope optics are not moving. 

Scope Mount Motion 

I have always been suspicious of scope mounts. These things take a heck of 
a beating on a high powered rifle, and I have never been certain that they 
stayed put. The mounts on this particular rifle are Weaver Top Mounts with 
aluminum bases attached by two 6-48 screws. Now, there is just no way that 
two small screws can keep these bases rigidly fixed to the receiver under the 
loading conditions present on a rifle, no matter how tight you get them. This 
becomes very evident when one realizes that the axial load on the scope is 
roughly 500 to 700 pounds on a 270 sporter during firing. Well, in fact the 
bases don’t stay put, and you can prove this with a very simple test. All you 
have to do is tap on the front base with a small hammer applied to a wood 
dowel so as to move it to the right, and repeat the operation on the rear base 
in a direction to move it to the left. Then you fire a shot, and repeat the 
operation three times for a three shot group. The whole operation is repeated 
again, only this time the bases are tapped in the opposite direction. If there is 
no effect, all six shots should be grouped together. When I ran this test, two 
distinct three shot groups resulted separated by 0.503 inches in the horizontal 


Rifle Accuracy Facts 

Figure 5-1 - Computer representation of an actual target showing two distinct 
groups caused by tapping the sight bases to skew the scope sight mount bases first 
to the left and then to the right. 

direction. A computer representation of this target is shown in Figure 5-1 . In 
order to get this large an error, the two bases need only move by ±0. 1 8 mils. 
Not very much motion, and about the amount of motion that might be ex- 
pected in a small screw. By the way, the screws were tightened by impact 
driving, which is the only way to get them really tight. I should also mention 
that I have tried several types of chemical bonding between the bases and the 
receiver, but they always shot loose. Of course, this problem is not the fault 
of the mount, but is the result of the way the receiver is designed to accept 
scope sight mounts. Some of the newer bolt action rifles have taken this into 
consideration, and have grooves milled into the receiver to accept a clamp-on 
mount. Hopefully, this design change should solve the problem. However, 
we are stuck with this problem on this particular receiver, and we want to 
eliminate it completely so that we can get on with our investigation of other 
problems. Consequently, I made copies of the aluminum bases using steel, 
and I used a low temperature (i.e. 430°F) silver solder to attach them to the 
receiver. Don’t confuse this stuff with ordinary solder, because it is much 
stronger, having a shear strength that can approach that of mild steel (i.e. 
15,000 psi). Just to be sure of the strength of the silver solder, I decided to 
test two different types of joints in a calibrated hydraulic press. The first was 
a lap joint, which had a shear strength of 4500 psi, and the second was a 
cylinder in a matching hole, which had a shear strength of about 14,000 psi. 


Chapter 5: Scope Sight Problems 

The scope sight base joint should have a strength that lies somewhere in 
between these values, because the two test cases represent the extremes in 
joint strength. Based on the hydraulic press test results, the minimum strength 
of the joint between the receiver and the bases should be about 8,000 pounds, 
which means that the silver soldered joint should withstand more than ten 
times the actual load. In fact, I test them by trying to knock them off with a 
hammer and a brass punch to make sure of the bond. This modification 
should only be made by a skilled gunsmith, because of the obvious possibil- 
ity of altering the heat treatment and the strength characteristics of the re- 
ceiver. After firing the rifle a number of times with silver soldered bases, the 
test depicted in Figure 5-1 was repeated, and there was no evidence of mo- 
tion of the bases. Now before someone notices the small size of the two three 
shot groups and decides that there is no point in going any further, the reader 
is advised that this test was run later after several other corrections were 
made to the experimental rifle. 

At this point in the experimental investigation I decided to build another rifle 
exactly the same as the 270 with silver soldered steel bases but chambered 
for 6mm Remington. The reason for doing this was that high quality match 
bullets were not available for the 270 but were available in 6mm. I knew that 
the ordinary 270 bullets that I was using were poorly balanced and contrib- 
uted a large error. It seemed like a good idea to try to minimize the bullet 
problem, at least for the time being, to help isolate some of the other prob- 
lems. This turned out to be a good move because the first set of groups 
revealed another scope mount problem. Figure 5-2 shows two groups fired 

Figure 5-2 - Typical 
6mm Remington 
targets fired with 
Cook match bullets 
showing vertical 
dispersion due to 
the axial load 
developed by the 
scope between the 
front and rear 
scope mounts. 


Rifle Accuracy Facts 

Figure 5-3 - Photograph 
of the hydraulic cyclinder 
used to impose a 
compression force of 
up to 200 pounds 
between the front and 
rear mounts. Muzzle 
deflection was measured 
by dial gages. 

with the 6mm using Cook 65 grain match bullets. You can see that the bullet 
holes are scattered in a string vertically and to the right. While a lot of things 
could cause this type of dispersion, it turned out to be differential axial mo- 
tion of the scope between the front and rear rings. This causes a differential 
compression or tension axial force to develop between the two rings. Ac- 
cording to a theoretical calculation the force could approach 200 pounds. 
This force warps the receiver causing the barrel to point in a different 
direction. Just to prove this theory I made a closed hydraulic cylinder with a 
pressure gage attached that replaced the scope (Figure 5-3). The action was 
held in a vise and a dial gage measured the deflection of the muzzle as the 
hydraulic fluid was heated causing a axial force between the front and rear 
scope mounts. The results are tabulated in the following table. 




Effect of Differential Force 
Between Scope Mounts 



Deflection (mils) 

Miss Distance 
@ 100 Yards(in) 






















Chapter 5: Scope Sight Problems 

Figure 5-4 - Photograph of the steel bridge mount on the rifle action, which was 
used to solve the scope mount axial differential loading problem. 

From the data you can calculate the angle with respect to the vertical to be 
about 23°, which is a little less than the angle seen on the targets. The reason 
for the groups being canted at an angle is that the receiver is weaker on the 
right side than the left as a result of the loading port. Consequently, the 
receiver bends in a plane canted to the right with respect to vertical. One can 
also see from Table 6 that a differential force of roughly 75 to 100 pounds is 
all that is required to cause the amount of linear dispersion seen in Figure 5- 
2. I decided that the easiest way to solve this problem was to make a steel 
bridge mount and silver solder it at both ends (Figure 5- 4). The bridge 
mount worked and eliminated the problem. I repeated the test in Table 6 with 
the bridge mount and the muzzle deflections were reduced by roughly a fac- 
tor of ten, which means that the vertical dispersion caused by the scope mount 
differential axial load should be less than 0.1 inch at 100 yards. The bad part 
about this solution is that it interferes with the loading port and is a bit of a 
nuisance. It also adds about 1.5 ounces of weight, but I don’t know of any 
other solution. However, the bridge mount does add considerable stiffness to 
the fairly flexible receiver, and should improve accuracy in other ways be- 
sides the scope problem. To further reduce the scope differential loading 
problem, I lubricated the clamp and saddle of the rear mount with a teflon 
lubricant (i.e. Friction Block) and didn’t tighten the screws quite as tight as I 
normally would. Whether or not this helped is not known, because the effect 
on group size was too small to be detected. 

There is one other source of scope sight motion that I discovered later in this 
work, and that is motion of the scope tube in the mounting rings. The bottom 
part of the scope mount that clamps onto the bases has a circular cradle de- 
signed to fit the scope tube. Unfortunately, the diameter of the circular cradle 


Rifle Accuracy Facts 

is about 5 mils too large, and the clamping band is too wide, so the scope tube 
is really only restrained in the horizontal direction by friction (see Figure 5- 
5). You might think that the clamping bands would distort the scope tube 
enough so that the tube would conform to the cradle, but this is not the case. 
The scope tube only deforms about one mil on the diameter when the bands 
are very tight. If the scope moves in one of the mounts just 0. 1 5 mils in a 
horizontal direction, the shot will be displaced by 0. 1 inch at 1 00 yards. While 
I was never able to prove conclusively that the scope tube was moving in the 
mounts, there were strong indications that it was moving and contributed as 
much as 0.3 inches of horizontal dispersion at 100 yards. The reason that this 
effect is difficult to prove is that wind effects get into the act, making it diffi- 
cult to be absolutely sure. You see, I didn’t have the tunnel range at this time. 
Fortunately, it is an easy problem to fix, as you can see in the drawing shown 
in Figure 5-5. All we have to do is scoop out the bottom of the circular cradle 
with a 3/4 inch ball end mill and the scope tube is then forced to contact the 
inside of the mounting ring at three points that are equally spaced. The amount 
of material removed by the ball end mill (30 mils) is exaggerated in the 
Figure 5-5 for the sake of clarity. Another method is to bed the scope tube in 
the bottom part of the mount with Devcon F aluminum fdled epoxy. I use 
black shoe polish instead of using other release agents, and hold the scope 



Figure 5-5 - Sketch of a Weaver top mount demonstrating a modification to the 
cradle to eliminate the two-point contact with the scope tube. 


Chapter 5: Scope Sight Problems 

onto the mounts with strong rubber bands until the epoxy hardens. Either 
approach, or both used together, will prevent the scope from moving in the 
mounts, and we can quit worrying about it. Other types of scope mounts may 
have this same problem. However, I doubt that this small effect can be ob- 
served in an ordinary sporter. 


Parallax is easily detected by moving the eye in a lateral direction behind a 
fixed scope, and observing motion of the reticule with respect to the target. It 
is a fact of optical principle that parallax can only be perfectly eliminated at 
one range for a given adjustment of a telescopic sight, and the higher the 
power the more critical the adjustment. Low powered scopes usually can’t 
be adjusted for parallax and are designed to be free of parallax at some aver- 
age range. High power (i.e. more than 9X) scopes have a special adjustment 
ring that is usually calibrated for range. Unfortunately, I can never seem to 
completely eliminate parallax in most high powered scopes (i.e. 20x to 36x) 
with the adjustment provided. Maybe you don’t have this problem, but if 
you do, you can eliminate it by moving the eye back beyond the optimum eye 
relief and centering the circle that appears in the scope field of view. This 
approach has the effect of keeping your eye centered on the optical axis so 
that parallax doesn’t matter. This has an additional advantage of reducing 
the chance of eye contact with the scope during recoil. 

Optical Refraction 

Optical refraction, which is more often referred to as mirage, occurs when 
there are small but significant density changes in the air space between the 
shooter and the target. These density gradients cause the light rays to be bent 
and distorted. As a result, the target image appears to move and may be 
distorted or blurred. Wind and high ambient temperatures usually make mi- 
rage worse, although, mirage can be severe under cold conditions. Mirage is 
usually worse close to the ground, and it is particularly bad over bare ground. 
The only really satisfactory way to deal with this problem is to pack up and 
go home and come back another day. However, we don’t always have that 
option, and with experience you can minimize the effect. 


Rifle Accuracy Facts 

There are really two types of mirage. One type is what I call shaky mirage 
which is rapidly changing and the other is a very slowly varying type of 
mirage that most shooters are unaware of. The shaky stuff is often caused by 
the hot air rising off a warm barrel right in front of the scope sight, although 
it can occur on a hot windy day by hot air boiling off the ground. If the shaky 
stuff is being generated by the barrel you can attach a piece of thin plastic 
about 3 or 4 inches wide over the barrel in front of the scope which deflects 
the warm air to the sides. Velcro is usually used for attaching the plastic sheet 
to the barrel and works well. The long tubes that screw into the objective 
lens cell of target scopes may help but can cause movement of the lens cell. 
For this reason most target shooters no longer use them. If the shaky mirage 
is caused by hot air beyond the muzzle there is another way to compensate. 
If you watch closely, you will be able to notice the occasional, momentary 
appearance of what appears to be a clear, well focused image. Well the trick 
is to get lined up on this real image and squeeze the trigger when the sight is 
lined up properly during one of these opportunities. 

However, other shooters use a different approach, and use the mirage as a 
wind indicator. The idea is to line up the cross-hairs on the clear image when 
the wind clears away the mirage and then fire when the mirage boils up and 
obscures the target. The theory behind this is that the cross wind is at a 
minimum when the mirage is at a maximum. This assumes that the gun 
doesn’t move while you are waiting for the mirage to boil, so it can’t work 
for anything but bench rest shooting. The only other solution that I know of, 
and it isn’t very practical, is to go shooting on the moon where there isn’t any 

The slow type of mirage is difficult to detect but it is present on open ranges. 
I built a mirage reference scope adjustable mount that holds a 36X target 
scope on the bench (Figure F-l, Appendix F). By watching the target through 
this scope you can tell if slow mirage is present and correct for it. In the 
Tunnel Range slow mirage can cause a drift in the vertical direction of 0.6 
inches without the exhaust fan. The exhaust fan essentially eliminates this 
problem if you match the outside air temperature with the tunnel 
wall temperature. 


Chapter 5: Scope Sight Problems 

Optical Resolution 

Optical resolution is one of the limitations on our ability to aim a rifle at a 
target. It depends on magnification, scope optics, atmospheric conditions 
and the diameter of the objective lens. Of course, it also depends on an 
individual’s visual acuity. Unfortunately, we don’t have a lot of control over 
most of these factors. While it appears to me that optical quality depends to 
some extent on price, most scopes these days have excellent optics. The 
diameter of the objective lens is fixed by the largest diameter objective tube 
that you can hang on a rifle without it becoming awkward and ungainly. 
Most spotting scopes have a larger objective than a rifle scope has, and you 
can tell the difference in resolution, at the same magnification, by simply 
looking at the same scene and comparing them directly. The diameter of the 
exit pupil, which is the diameter of the column of light that comes out of the 
eyepiece and enters the eye, is equal to the diameter of the objective lens 
divided by the magnification (i.e. power). This means that the higher the 
magnification the smaller the exit pupil becomes. Ideally, the scope exit 
pupil diameter should match the diameter of the pupil of the eye for maxi- 
mum illumination. In dim light, the pupil of the eye may have a diameter of 
5 mm or larger, while in bright light it may shrink down to 1 or 2 mm. Con- 
sequently, hunting scopes are generally designed to have an exit pupil of 
around 5mm, while target scopes usually have an exit pupil of around 2 mm. 
An example is the Leupold 20X shown on the rifle in Figure 2-1. This scope 
has an objective lens diameter of 40 mm, and consequently, at a power of 20 
has an exit pupil of 2 mm. What all this amounts to is that you can improve 
resolution by increasing magnification up to the point where the exit pupil 
becomes too small for the lighting conditions. 

Determining the optical resolution of a scope is an “iffy” proposition, and 
depends a lot on viewing conditions, but my best guess is that it is around 10 
mils at 1 00 yards with a 36 power scope under good conditions. It also seems 
to me that resolution is roughly proportional to magnification, as long as the 
exit pupil remains about the same. This means that our aiming accuracy can 
be no better than maybe 10 mils, and is enlarged by the things that we have 
previously discussed. Of course, another factor is the visual acuity of the 
individuals eyeball. Shooting accuracy, which is the accuracy with which 
one can aim the rifle and release the trigger without disturbing the alignment 
of the rifle, is discussed later in the book (Chapter 11). 


Rifle Accuracy Facts 




I t would hardly seem possible that the threaded barrel joint could move, 
causing the barrel to point in a slightly different direction after a shot is 
fired. But, that is exactly what happens, and barrel joint motion can cause 
large flyers (i.e., one inch or more) in a group. The only things that prevent 
motion of the barrel joint is the lateral friction forces caused by the axial 
preload that results from the applied torque on the barrel when it is installed 
and the stabilizing forces acting on the angular surfaces of the threads. 
Unfortunately, applied loads (e.g., bolt thrust during firing), and differential 
thermal expansion can either reduce the axial preload or completely over- 
whelm the stabilizing effect of the axial preload. Under some temperature 
conditions, such as rapid fire, it is possible for the joint to be completely 
unloaded or loose when the gun is fired. So how do we know that the joint is 
moving? We make some measurements. 

Barrel Joint Motion Measurement 

All of the experimental measurements will be made on a Remington 721 
action with a barrel chambered for the 270 Winchester cartridge. This action 
has a 1.0625X16 thread. What we need is some simple way to determine 
which way the barrel is pointing with respect to the receiver after each shot. 


Rifle Accuracy Facts 

Figure 6-1 - Photograph showing Weaver K12 scope mounted on a mandril that 
slips into muzzle. By comparing aiming point on the target of the muzzle scope with 
the regular scope mounted on the receiver, motion of the barrel joint between shots 
can be detected. 

Well, the simplest way that I can think of is to attach a second scope sight to 
a mandril that slips into the bore, which tells us where the barrel is pointing. 
The rifle has to be mounted on a machine rest for this experiment. The test 
routine is to adjust the machine rest so that the receiver scope is pointing at 
the aiming point, and then insert the muzzle scope in the muzzle and adjust it 
so that the cross hairs are also on the aiming point. After the shot is fired the 
machine rest is checked to make sure that the receiver scope is still pointed at 
the aiming point, and then the muzzle scope is inserted and the position of 
the cross hairs relative to the aiming point recorded. In this way you can tell 
where the barrel is pointing with respect to the receiver. The muzzle scope 
fixture is shown in Figure 6-1 with the 12 power scope attached. The radial 
clearance between the mandril and the bore is 0. 1 mils, which is a fairly tight 
fit. With this clearance the pointing error of the scope is ±0.3 inches at 100 
yards. So, while this is a simple approach that works, it is also a little crude. 
A series of four 5 shot groups were fired. The data from the muzzle scope 
confirmed that when a significant flyer appeared, the barrel was pointing in a 
new direction relative to the receiver after the previous shot. The next shot 
would then be a flyer. The barrel would occasionally stay put after firing a 
shot, but it would move fairly often and return to the original position after 
firing the next shot which would be a flyer. As you would expect, significant 
barrel motion was not always observed from shot to shot because the motion 
would be too small to detect due to the imprecision of this measurement 
method (±0.3 inches). The magnitude and direction of the shift in barrel 
position was in general agreement with the position of the bullet impacts. I 


Chapter 6: Barrel-Receiver Threaded Joint Motion 

can’t think of any sensible way to present the data in graphical form, so you 
will just have to take my word for it that the data proved that the barrel joint 
was moving. A more precise way to perform this experiment might be to 
permanently attach a laser to the bottom of the barrel near the muzzle. Then 
one could observe the position of the laser spot on the target compared to the 
bullet impact as the rifle was fired. 

I ran another simple experiment to prove that there is relative motion in the 
threaded joint between the receiver and the barrel. I had previously noted 
that the first few shots from a newly installed barrel were always wild. These 
first shots were much too far out of the normal group to be caused by a clean 
barrel. It would seem that this would have to be due to the barrel shifting 
position in the joint at the first shot. I removed the barrel and applied Perma- 
nent Loctite, which is a thread locking material, to the threads and replaced 
the barrel. When I test fired the rifle the first rounds were not wild, and the 
5 shot group measured 0.626 inches at 100 yards. After a few more rounds 
were fired, fliers started appearing, indicating that the Loctite was no longer 
able to constrain the barrel joint. Epoxy is not strong enough to take the 
repeated stress of firing, particularly at elevated temperatures. This experi- 
ment also proved to me that the barrel joint can move. 

The upshot of all this is that I think we can safely assume that there is relative 
angular motion between the barrel and receiver. We are going to measure the 
axial preload that is actually applied to the joint when it is tightened, so that 
we can see if the joint is tight enough to withstand the loads caused by firing. 

Barrel Joint Axial Preload Measurements 

Fortunately, it is fairly simple to measure the joint axial preload with a strain 
gage. We do it just like we did when we measured the bolt thrust, except the 
gage is placed over the threaded portion of the forward receiver ring. With 
ordinary 10-30 motor oil as a lubricant, the axial preload measured 10,600 
pounds when the barrel was tightened with an applied torque of about 250 ft- 
lbs. This value is consistent with the calculated value of 10,506 pounds for a 
friction coefficient of 0.24, and an applied torque of 250 foot-pounds. The 
friction coefficient is a number that when multiplied by the axial preload 
yields the lateral friction force. Once the lateral friction force is known you 


Rifle Accuracy Facts 

can determine the torque required for a given axial preload. The 
calculated value for the axial preload can be obtained from a textbook 
equation. The equation for calculating axial preload is 

F = (12*T)/(P/(2*tc) + f*Rt/cos p + f*Rb) 


F = axial preload, pounds 
P = thread pitch, inches, (1/16) 

7t = 3.14159 

f = friction coefficient, pounds/pound, (0.24) 

Rt = average radius of the barrel threads, inches, (0.505) 

Rb = average radius of barrel shoulder, inches, (0.565) 

P = thread angle, 30 degrees on standard threads 
T = applied torque, foot-pounds 

The friction coefficient of 0.24 is consistent with handbook (Handbook of 
Physics and Chemistry) values for petroleum lubricants, although it is only 
approximate. The friction coefficient also depends on the surface finish which 
is difficult to evaluate. In this case the lateral friction force acting on the 


















I — 






E = 30,000,000 PSI FOR STEEL 



Figure 6-2 - Graph showing how stress (load) is related to strain (stretch) 
for steel. 


Chapter 6: Barrel-Receiver Threaded Joint Motion 


Barrel-Action Joint Tests 

Test Lubrication 













Large flyers under all 
cartridge case and 
temperature conditions. 








First two groups were 
excellent, but recoil lug 
failed in compression 
and remaining groups 
were bad. 






Accuracy excellent. 
Axial preload stayed 
the same within 
the accuracy of 






Good accuracy. Axial 
preload reduced 
during firing. 






Very poor accuracy. 

threads would be 10,600 times 0.24, or 2,544 pounds. So, we have a mea- 
sured value for the threaded joint axial preload that is consistent with theo- 
retical calculations. This value of 1 0,600 pounds is probably representative 
of the axial preload found on most sporters. However, I did measure the 
axial preload on one standard Remington 721 with strain gages when the 
barrel was removed and measured a value of 8054 pounds. Well 10,600 pounds 
seems like a lot, and you might think that a load that large should freeze the 


Rifle Accuracy Facts 

barrel joint. It probably would if it weren’t for the other effects during firing 
that reduce the axial preload and friction forces acting on the joint. 

Barrel Joint Tests 

In order to determine the effect of different joint conditions, a number of 
experimental tests were run to determine the effect of the friction coefficient 
and axial preload. These tests on the 270 sporter are summarized in Table 7. 

Some yielding of the first two barrel threads was observed on tests 2 and 4. 
In order to explain the terms yield and failure a graph is shown in Figure 6-2. 
Visualize a steel bar that is being stretched by equal tensile forces on each 
end which produces a stress in pounds/square inch. Stress is shown on the 
vertical axis. The amount of stretch of the bar or strain in inches per inch of 
bar length is shown on the horizontal axis. Steel is an elastic material and the 
stress is proportional to the strain until the steel reaches the elastic limit and 
starts to yield. The bar will continue to support a higher stress for a while 
until it reaches the ultimate stress and fails (breaks). One should be careful 
about overloading the threads and barrel shoulder when using Teflon tape or 
lanolin with the standard V type threads. Standard V type threads won t 
support an axial preload in excess of 20,000 pounds before they start 

The approximate friction coefficients for the lubricating materials for steel 

on steel are 





10-30 oil 






Several facts can be determined from the test results. It can be seen from 
tests 2, 3, and 4 that the joint can’t sustain an axial preload above about 
20,000 pounds without failing. Another conclusion can be reached, and that 
is, an axial preload of at least 25,000 pounds on the joint is required to stabi- 
lize the joint under all conditions when the joint is lubricated with a low 
friction coefficient lubricant. However, tests 2 and 4 demonstrate that an 
axial preload of 25,000 pounds cannot be sustained by the joint as presently 


Chapter 6: Barrel-Receiver Threaded Joint Motion 

Now, there are two things that stabilize a given threaded joint, the axial preload 
and the lateral friction force. Unfortunately, it is difficult to determine the 
relative importance of these two effects. So, at this point (Test 5), I decided 
to increase the lateral friction force by using rosin as a thread lubricant, and 
I installed a recoil lug that was heat treated to 1 30,000 psi yield strength. The 
new recoil lug was necessary because the factory recoil lug is not strong 
enough to withstand these large preloads. By the way, the action is factory 
heat treated to a yield strength of about 190,000 psi, and the barrel is factory 
heat treated to about 130,000 psi. I intended to apply an axial preload of 
about 20,000 pounds, but could only reach 17,800 before breaking the action 
wrench, which was made of mild steel. Just how large a friction coefficient 
rosin has I don’t know, but it must be a lot greater than the friction coefficient 
of dry steel on steel (0.58), because it is used on the jaws of the barrel vise to 
keep the barrel from rotating during barrel installation. Lanolin was used on 
the barrel shoulder to reduce the torsional load imposed during tightening 
the barrel. The result of Test 5 was that the accuracy was very poor, which 
indicates to me that the main force that stabilizes the joint is the axial preload, 
and that the lateral friction force plays a secondary role in keeping the joint 
rigid. However, the axial preload of 25,000 pounds required to stabilize the 
joint is more than the standard V threads will take without yielding. At this 
point I decided to stop and analyze the loads acting on the joint, because this 
is a real design dilemma. 

Barrel Joint Loading 

There are several loads acting on the barrel joint that can reduce the axial 
preload. One of these effects is the differential heating between the barrel 
and the receiver ring, which can be substantial. By using a thermistor, I 
measured a temperature difference of 56°F between the inside of the cham- 
ber (133°F) and the outside of the receiver (77°F) after firing 15 rounds in 
rapid succession. One can calculate that this temperature difference between 
the barrel and receiver will cause enough differential expansion in the axial 
direction to reduce the axial preload on the joint by roughly 7,000 pounds. 
Radial expansion of the barrel reduces this effect by some small amount that 
I don’t know how to estimate, so we will stick to the 7,000 pounds. There is 
no doubt in my mind that an average temperature difference of at least 56°F 


Rifle Accuracy Facts 



1800 • ■> * 

1400 . 

• ■> 


^4000 „ 


_ 32pO.. = 5 ri BUUE T. 


1800*- > .. ,.gPPi>*^ L 

_uuu^. t 


IL, " 800 





Figure 6-3 - Drawing showing inertial forces due to recoil motion of the barreled 
action and force due to bolt thrust acting on the barrel joint. 

can and likely does occur during rapid firing. There is so much time lag 
involved in making the temperature measurements that the temperature dif- 
ferential is probably greater. While you are waiting for the thermocouple 
used to measure the local temperature to reach equilibrium the barrel and 
action temperatures are gradually equilibrating. Consequently, the measured 
differential temperature between barrel and receiver will be less than the ac- 
tual difference in temperature. 

Another thing that effects the load on the joint is the action of the cartridge 
case during firing. We know from Chapter 4 that the bolt force can vary from 
1,000 to 7,200 pounds. This is due to the variation in the headspace and 
cartridge case conditions, causing a difference in the load on the joint. The 
diagrams shown in Figure 6-3 show the component forces acting on the joint 
for the two extreme cartridge case conditions of maximum and minimum 
bolt force. The dashed lines show the magnitude of the acceleration forces 
and the solid lines show the component forces resulting from the cartridge 
case. The heavy solid vectors show the direction and magnitude of the re- 
sultant forces acting on the threads. The reader should note that all applied 


Chapter 6: Barrel-Receiver Threaded Joint Motion 

forces are opposed by a reaction force caused by the recoil acceleration. I 
have called these reaction forces acceleration forces. It can be seen that in 
the maximum bolt force case (top diagram) the threads have an additional 
tensile force of 5,400 pounds acting on them. In the minimum bolt thrust 
case (bottom diagram) the threads have a compression force of 800 pounds 
acting on them as a result of the cartridge case forces. Recall that the tension 
force (5,400 pounds) derived from the axial preload stabilizes the joint and 
the compression force (800 pounds) destabilizes the joint. However, this 
only occurs during the time the chamber is pressurized and the direction of 
the force will reverse when the chamber pressure drops. What this means is 
that the large stabilizing force of 5,400 pounds can reverse sometime after 
the bullet leaves the muzzle and become a 5,400 pound destabilizing force. 
We don’t know when the joint actually moves. It is most likely happening 
shortly after bullet exit, because that is when the loads that reduce the axial 
preload appear to be the largest. This is also borne out by the muzzle scope 
tests where the barrel is observed to move after a shot that was in the group, 
but the next shot would be wild. 

There is another dynamic load that acts in a similar manner to the bolt thrust, 
that is due to chamber radial expansion from the chamber pressure. One can 
calculate that this radial expansion produces an axial tension load of some- 
where between 8,250 and 11,512 pounds depending on the degree of con- 
straint provided by the forward receiver ring. The correct value is probably 
somewhere in between, so let’s assume a value of 10,000 pounds. 

In addition, there is an impact force on the joint when the recoil lug impacts 
the stock in a standard sporter. You may recall that this was measured back in 
Chapter 4 and found to be 1,500 pounds. This is probably a lesser effect on 
bench rest actions that use pilar or glue-in bedding. Also, the recoil force is 
less on the 6PPC than the 270 Winchester. However, there must be some 
“recoil lug” force still acting on bench rest rifles because the recoil force 
must be transmitted from the action to the stock. 


Rifle Accuracy Facts 

If we sum up all these destabilizing loads from different sources for the case 
of a cold and a hot barrel we get: 

Cold Barrel 

Recoil lug 


Bolt thrust 


Chamber radial expansion 




Hot Barrel 

Recoil lug 


Bolt thrust 


Chamber radial expansion 


Differential temperature expansion 




What all this comes down to is that the joint with an axial preload of 20,000 
pounds has marginal stability under ordinary conditions, and is unstable when 
hot after firing two or three 5-shot groups without cooling. This roughly 
corresponds with our experience shown in Table 5, so I feel certain that it is a 
real effect. What is needed is an axial preload in excess of 24,000 pounds to 
assure that the joint cannot move under these extreme conditions of heating, 
shock, and vibration. 

Figure 6-4 - Drawing of the standard Remington 721 barrel joint design with 
National Form 60° V threads and recoil lug. It is equivalent to a standard bolt and 
nut joint, where the recoil lug serves as a washer. 


Chapter 6: Barrel-Receiver Threaded Joint Motion 

Figure 6-5 - Photograph of a plastic model of the barrel joint threads (standard V 
thread), using polarized light, which demonstrates how the load on the threads is 
concentrated on the first few threads near the front of the receiver (bottom right). 
Top photo shows the threads in the unloaded condition. 

Joint Redesign 

We have already redesigned the recoil lug to take the higher loads by making 
it out of a stronger steel (4140) which can be heat treated to a higher yield 
strength ( 1 30,000 psi). The commercial lug appears to be stamped out of a 
mild steel, which can’t be heat treated much above 60,000 psi. I also silver 
brazed the recoil lug to the front of the receiver (Figure 6-4). This was done 
primarily as a convenience to keep the lug from rotating during all the barrel 
changing that had to be done. However, it may have some effect on joint 
stability, and I believe this should be done during manufacture. The barrel 
shoulder will take a load of about 32,000 pounds before yielding, so we will 
try to come up with an improved thread design that will stand an axial preload 
of this level. 


Rifle Accuracy Facts 

Figure 6-6 - Theoretical calculation of the individual thread load as a percentage of 
the total preload. The front of the receiver is on the right of the figure. Only the first 
few threads carry a significant load. 

Standard National Form V Thread 

The standard National Form V thread used on this joint is the same thread 
that is used on most bolts and nuts. While this is a well known situation 
(References 18,19) in mechanical engineering circles, it will likely surprise 
the reader to find out that the individual threads are not equally loaded. It 
turns out that a large percentage of the total axial preload is carried by the 
first few threads next to the front of the receiver. This is demonstrated in 
Figure 6-5 which shows the result of a photoelastic test. The threads are 
machined into two plastic sheets that are 1/8 inch thick. The threads are four 
times the size of normal 16 thread per inch threads found on the Remington 
action (i.e., 4 threads/inch). The two pieces are held in a fixture while a force 
is applied to the right side of the top piece acting to the left, and an opposing 
force acting to the right is applied to the bottom piece. The test is run using 
polarized light, which is distorted by stresses in the plastic caused by the 
load. The plastic model is back lighted and is sandwiched between two pieces 
of polarized film. The two films are rotated relative to each other until the 


Chapter 6: Barrel-Receiver Threaded Joint Motion 

maximum effect is obtained and then photographed. Tension stresses show 
up as a dark area and compression stresses show up as a light area. Both the 
unloaded case (top) and loaded case (bottom) are shown in the figure, and it 
can be seen that most of the load is taken up by the first few threads near the 
front of the receiver. Obviously, the threads toward the chamber end of the 
barrel on the left side of the figure are essentially unloaded. The load on each 
thread in terms of percentage of the total load was calculated using the method 
of Bluhm and Flanagan (Reference 19) and is shown in Figure 6-6. You can 
see that the first thread nearest the front of the receiver carries about 36% of 
the total load, while the last several threads carry only a small percentage of 
the total load. This explains why the joint is really not “frozen” at all, and is 
relatively free to move, because only the first three or four threads carry a 

Figure 6-7 - Sketch of 
the Spiralock™ ramp- 
thread. The width of the 
30° ramp is 0.025 inch 
compared to the pitch 
or width of the thread 
of 0.0625 inch. Only 
the peaks of the receiver 
threads are loaded. 

The threads are shown 
in the loaded condition. 
The front of the receiver 
is to the right. 

Figure 6-8 - Photograph of plastic model of the barrel joint showing how the ramp- 
thread has more evenly loaded threads, which allows the preload on the joint to be 
increased. Front of the receiver is on the right. 


Rifle Accuracy Facts 



Figure 6-9 - Calculated individual thread load for the Spiralock™ ramp-thread in 
terms of percentage of total preload. The load distribution is much more evenly 
distributed than was the case with the standard thread (Figure 6-6). 

significant axial load. If the threads at the rear end of the barrel were loaded 
to roughly the same extent, then the barrel joint would not be as likely to 
rotate about a lateral axis and would be more likely to stay aligned with the 
receiver. The first thread carries a load of 7,200 pounds with an axial preload 
of 20,000 pounds. Since we found out that this is the axial preload level 
where the threads first start yielding, we could theoretically load this joint up 
to 79,200 pounds if the load distribution on all eleven threads was perfectly 
even! This is an impractical load level because the barrel shoulder would 
fail. Fortunately, there are at least three ways of improving the load distribu- 
tion on the threads. 


Chapter 6: Barrel-Receiver Threaded Joint Motion 


A sketch of the ramp-thread, which is a patented thread design called 
Spiralock™ by Detroit Tool Industries, is shown in Figure 6-7. A photoelastic 
experiment performed by the author (Figure 6-8) shows that the threads are 
more evenly loaded than the previously tested standard V thread. Data sup- 
plied by Detroit Tool Industries were used to calculate the load distribution 
shown in Figure 6-9, where it can be seen that the load distribution is much 
improved. For instance, the first thread only carries 13.7% of the load com- 
pared to 36% for the standard thread. Also, the threads toward the chamber 
end of the barrel carry a much larger percentage of the average load. Well, I 
machined a new barrel (chrome moly 4140) with the ramp-thread and in- 
stalled it with a measured axial preload of 32,000, using Teflon tape as a 
lubricant and a torque of about 200 foot-pounds. After firing 50 rounds the 
axial preload had dropped to 29,000, and there was no visual observable 
evidence of metal yielding (i.e., permanent deformation). This 10% loss in 
axial preload is probably due to small local yielding at stress concentrations, 
and is to be expected with a new threaded joint. The ramp thread joint was 
reassembled with an axial preload of 3 1 ,000 pounds and test fired again at a 
rapid rate to heat the barrel. The wild flyers that had been present at elevated 
temperatures with the standard V thread were eliminated, indicating that this 
joint design is successful. Since the ramp thread can be cut on the barrel with 
a die or with an ordinary threading tool modified to have the ramp shape, this 
design modification is practical in production. Barrel replacement by gun- 
smiths is also practical. Tolerances are not any more critical than on the 
standard V thread. This approach was suggested by my son, who is a me- 
chanical engineer. Since some of the patents on this thread are still in force, 
Detroit Tool Industries may require a patent release for large scale produc- 
tion. However, the President (Mr. Ed Palm) of Detroit Tool Industries 
(1-800-521-2688) assured me that they would not object to custom gunsmiths 
using this thread. There is another approach that is probably not patentable, 
and that is a variable depth thread similar to a pipe thread with much 
less taper. 


Rifle Accuracy Facts 

Variable Depth Thread 

The reason that the standard V thread doesn’t have a uniform load distribu- 
tion, is that when the joint is tightened the barrel stretches and the receiver 
compresses in the longitudinal direction. This causes the threads toward the 
chamber end of the barrel to be unloaded. While this only amounts to 0.5 mil 
(1 mil total difference between receiver and barrel), it is enough to almost 
completely unload the last thread. What we need is a thread that starts being 
loaded on the end of the barrel, and as the joint is tightened, transfers some 
load to the threads near the front end of the receiver. A friend of mine (John 
Weydert) who is a mechanical engineer, suggested machining the threads in 
the barrel at the front of the receiver a little deeper than those on the chamber 
end of the barrel, using a linear taper. I made calculations that predicted that 
a variation in thread depth of 2.5 mils/inch would result in uniform loading 
for an axial preload of 30,000 pounds. The amount of taper depends on the 
cross section area of the barrel tenon. This thread is easily machined on a 
lathe using a taper attachment. However it would be easier and better to cut 
the tapered thread in the receiver during production using a tapered tap. A 
photoelastic test of the tapered depth thread (Figure 6-10) showed that the 
load on the individual threads was fairly uniform. You can see in the photo- 
graph that the clearance between the threads on the right side of the figure 
(receiver front end) is greater than on the left, which corresponds to the end 
of the barrel. The variable depth is much exaggerated in this figure, because 
plastic is much more elastic than steel. There is no point in a theoretical 
calculation, because it will simply predict a constant load of 9. 1% of the total 

Figure 6-10 - Photograph of plastic model of the barrel joint showing how the 
tapered-depth thread has more evenly loaded threads, which allows the preload 
on the joint to be increased. Notice the greater depth of the threads at the front 
of the receiver on the right side. 


Chapter 6: Barrel-Receiver Threaded Joint Motion 

load per thread. On the strength of this photoelastic test, I decided to ma- 
chine another barrel and install it on another used Remington 721 action, that 
I had purchased, for testing. The barrel with the variable depth thread was 
installed with an axial preload of 27,200 pounds. After firing, the axial preload 
dropped to 24,500 pounds, which seemed to be the maximum axial preload 
that this thread will sustain. This is not as good a design as the ramp thread, 
but it is better than the regular V thread. After this test I decided to stay with 
the ramp thread, because I know it works. 

Ramp Thread Accuracy Test 

The accuracy was tested and the average group size was essentially the same 
(0.884 inches) as that presented in Table 4 in a previous chapter (Chapter 4). 
There were no large flyers at high temperatures like there were before the 
new ramp-thread joint was installed. In the previous accuracy test the gun 
was cooled after every other group (i.e. 10 shots), where this time I fired four 
5-shot groups rapidly before cooling and cleaning. 

Figure 6-11 - Cross-section drawing of a barrel joint design that does not depend 
on a large preload for stability and is not affected by temperature gradients. 


Rifle Accuracy Facts 

Figure 6-12 - Photograph of an action showing a disassembled barrel joint design 
that is immune to temperature and other barrel joint problems. This design is also 
depicted in Figure 6-11. 

Complete Barrel Joint Redesign 

A sketch of an improved barrel joint design is shown in Figure 6-11, and a 
photograph of a receiver and barrel incorporating the improved design is shown 
in Figure 6-12. The collar on the barrel is clamped between a shoulder in the 
receiver and the threaded retainer ring. Consequently, thermal expansion of 
the barrel or collar in the axial direction simply increases the force holding 
the joint together instead of relieving the force as it does on the normal barrel 
joint. In other words, when the barrel heats up as a result of rapid firing or 
the barrel stretches as a result of the action of the cartridge case, the joint just 
gets tighter. This design is a much more reliable approach because it doesn’t 
depend to any great extent on the magnitude of the axial preload. As long as 
the retaining ring is reasonably tight the barrel is locked in place. The fact 
that the design works was proven with the hardware shown in Figure 6-12. 
This particular receiver and barrel could be fired with the scope on either the 
receiver or on the heavy barrel. The barrel measured 1 .2 inches in diameter 
at the chamber end and 0.9 inches at the muzzle. The average 5-shot group 
measured 0.65 inches and there was no difference in group size between the 
two scope locations. This is strong evidence that this barrel joint design is 
stable and does not allow motion between the barrel and the receiver 
between shots. 

There is one other way of preventing barrel joint motion and that is to make 
the receiver and barrel out of one piece of steel. The most accurate commer- 
cial rifle that I ever had (Savage Model 23D in 22 Hornet) was made this 
way. Unfortunately, this is impractical because you can’t replace the barrel. 


Chapter 6: Barrel-Receiver Threaded Joint Motion 


It was demonstrated that the standard V thread barrel joint was moving. Also, 
the barrel motion was particularly severe under the high temperature condi- 
tions obtained by rapidly firing 1 5 rounds, which caused large flyers. Theo- 
retical calculations as well as experimental measurements indicated that the 
barrel joint could move when the barrel was hot if the axial preload was less 
than 24,000 pounds. This problem was corrected by changing to a ramp- 
thread that allowed increasing the sustained joint axial preload from 20,000 
pounds to around 30,000 pounds. The increased axial preload obtained with 
the ramp-thread prevented any barrel joint motion. 

The question will arise as to whether all threaded barrel joints move in bolt 
action rifles. Obviously, no one knows, but I think it is likely that all bolt 
action rifles with threaded barrel joints probably do move to some extent, 
although those actions with integral recoil lugs and standard bedding prob- 
ably are less effected. O’Connor bedding, which was discussed back in 
Chapter 4, may stabilize the joint to some extent. O’Connor bedding applies 
a preload to the joint which likely stabilizes it. Most engineers know that it is 
very difficult to make a rigid threaded joint, particularly under the tempera- 
ture, shock and vibration conditions present in a rifle. 

Bench rest rifles have heavy barrels which conduct the heat away from the 
barrel joint reducing the effect of temperature. Also the heavy barrel helps 
reduce the load on the joint. They often have the receiver bonded to the stock 
reducing the effect of recoil on the joint. These features coupled with the fact 
that smaller calibers are usually used, and the barrels are cleaned frequently 
allowing the temperature differential to equalize, reduce the probability of 
barrel joint motion on bench rest rifles. However, barrel joint motion is a fact 
of life and it can be present to some degree in any rifle. I am very suspicious 
of the short handled action wrenches used by bench rest shooters to install or 
change barrels. These short wrenches make it impossible to apply sufficient 
torque to obtain a satisfactory axial preload with ordinary lubrication. In- 
creasing the axial preload by using Teflon tape as a lubricant will reduce the 
tendency of the barrel joint to move. Using Teflon tape and the same applied 
torque would more than double the axial preload. 


Rifle Accuracy Facts 


M ore than thirty years ago a friend of mine (Ed Cave) and I were camped 
in a mountain meadow covered with tall green grass. Green grass is 
pretty unusual in this part of the world (New Mexico). I decided to shoot at 
a target on a distant mountain side, so 1 sat down and fired several rounds 
over the grass. My friend was standing behind me, and when I had finished 
shooting he said, “Something funny is going on — sometimes I don’t see the 
muzzle blast on the grass and at other times it appears off to the left or to the 
right and sometimes right in front of you.” Well normally I would have an- 
swered “Uh huh” and gone on shooting, but I knew this guy was an accurate 
observer. So, I asked him to fire a few rounds so that I could watch, and sure 
enough he was right. It was pretty clear that the direction of the muzzle blast 
varied a lot from shot to shot. Well, that experience has bothered me for 
years, so I decided to find out just what the heck was happening. The first 
thing to do was to repeat the “grass” experiment in a more professional man- 
ner, and try to get some presentable data. Since I am an old aerodynamicist, 
I decided to use an “Old Aerodynamicist’s Trick.” Back in the good old days, 
when we couldn’t tell what was going on in an airflow problem, we used to 
attach things called tufts to a wing or some other shape, which allowed us 
to tell which way the wind was blowing. These tufts were made of two or 
three inch lengths of wool yarn. They would follow the direction of local air 
flow, and were very helpful in diagnosing aerodynamic problems. 
Sometimes, hundreds of tufts were required. These days computers are used 


Rifle Accuracy Facts 

to simulate the flow, and usually do a better job. I decided to apply the old 
tuft technology to the muzzle blast problem, because it is simple, cheap, and 
you can get photographic data. 

Figure 7-1 - Diagram of the muzzle blast flow field showing essential features. 

• Mi 


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Figure 7-2 - Photograph of the tuft 
screen showing centrally located 
muzzle blast. Screen is 4 feet square 
and was placed 18 feet from the 
muzzle. The circular pattern around 
the jet impact in the center results 
from an annular vortex ring, similar 
to a smoke ring. 

Figure 7-3 - Photograph of tuft screen 
where the muzzle jet was deflected 
up and to the left. A segment of the 
vortex ring extends from lower left to 
upper right. 


Chapter 7: Muzzle Blast 

Tuft Screen 

A four foot square frame was built of 1X6 inch wood with 2X4 inch screen 
wire attached to the front of the frame. A white sheet was attached to the rear 
of the frame to enhance the photographic contrast. The tufts were made of 1 
inch wide black paper. They were attached to the wire grid by bending the 
paper over the wire and fastening with Scotch tape. A bullet was fired through 
the center of the screen, which was placed about 1 8 feet in front of the muzzle, 
and the screen was photographed with a Polaroid camera. The idea was that 
the tufts would be displaced to the rear by the muzzle jet and its associated 
flow field. We should then be able to determine the location of the center of 
the muzzle blast flow field from the photographs. Figure 7-1 shows a simpli- 
fied sketch of the muzzle blast flow field. This flow region is called the 
transitional ballistics region between internal and external ballistics. When 
the hot, high pressure gas exits the muzzle it expands and the flow becomes 
supersonic. As the gas expands it slows down to sonic velocity (Mach num- 
ber one) and generates a thick shock wave called a Mach disk. The jet veloc- 
ity at the Mach disk is roughly 4000 fps because the temperature is high 
(~6000°F) and the speed of sound is high. This high speed flow generates a 
vortex ring similar to the smoke rings that smokers sometimes make. The 
muzzle blast shock wave, which produces the loud noise when you fire a 
rifle, continues to expand and eventually becomes a weak sound wave. The 
jet and the vortex ring continue to travel for some distance (at least 20 feet) 
and these are what we see hitting the tuft screen. Figure 7-2 shows a photo- 
graph of the tuft screen where the muzzle jet has hit the center of the screen. 
If you look closely you can see a rough circular pattern around the center of 
the screen. This circular pattern is caused by a vortex ring that forms around 
the jet in the center. Figure 7-3 shows a case where the muzzle jet has hit the 
upper left corner of the screen, and a portion of the vortex ring can be clearly 
seen extending from the lower left to the upper right. This indicates a jet 
angle of about six degrees from the bore axis. The next figure (Figure 7-4) 
shows a case where both the jet and the vortex ring completely missed the 
screen, which requires a muzzle jet angle of at least 12 degrees. The white 
square in the center of the screen was the aiming point where there are no 
tufts. Four different brands of 270 bullets were used, and all but one had 
large jet deflection angles. Missing the screen entirely was the most typical 
result, and it indicated that I should have used a larger screen. However, this 
size screen involved making 284 tufts, which was a lot of work. It probably 


Rifle Accuracy Facts 

iimnwiTniii i mi. 

■ Ill till Illlllll I II 1 1| 
nniiiiiii iiiiiii 

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would have been better to take high 
speed motion pictures of each shot, and 
make a print of the frame that occurred 
at the optimum time. However, I think 
that the results are good enough to 
show that the muzzle jet was not cen- 
tered with some bullets. This verifies 
what my friend and I observed while 
firing over grass a long time ago. I 
should point out that the tufts do not 
respond to the shock waves generated 
at the muzzle, but do respond to the jet 
issuing from the muzzle and the vor- 
tex ring, which slow down rapidly. The 
only reason for doing this experiment 
was to show the reader that the muzzle blast could be asymmetric with 
respect to the bore axis at some distance from the muzzle, because the data 
are useless as far as predicting the effect on bullet dispersion. But first, what 
could be causing this problem? 


iiiiiii imi 


Figure 7-4 - Photograph of the 
tuft screen showing a case where 
the muzzle blast missed the 
screen entirely. 

Bullet In-bore Cant 

The only logical way for the muzzle blast shock wave pattern to be asym- 
metrical with respect to the bore axis is for the base of the bullet to be canted 
when it exits the bore. The most likely way for the base to be canted is for the 
bullet to be canted while it is in the bore. I had observed unequal circumfer- 
ential rifling engraving on recovered cannon shells, which confirmed the fact 
that cannon projectiles can cant in the bore. However, I was reluctant to 
believe that a standard tangent ogive-cylinder (see Figure 7-5) rifle bullet 
shape could cant or tip in the bore. So, I decided to inspect some of the 270 
bullets to see if there was some defect in the shape of the bullets that would 
allow them to cant while in the bore. 

A number of bullets from different manufacturers were examined. Practi- 
cally all of them had a conical or ogive shaped afterbody instead of a true 
cylindrical shape. The afterbody is the rear portion of the bullet that extends 
forward from the base to where the ogive starts tapering. A conical or 


Chapter 7: Muzzle Blast 


Figure 7-5 - Drawing showing the geometry of a tangent ogive bullet shape. 

tapered afterbody will certainly allow a bullet to tip when it travels down the 
bore. On many bullets the ogive shape continues aft to the base and there is 
no cylindrical afterbody. My guess is that the manufacturers do this to make 
it easier to eject the bullets from the forming die. Having made a few bullets, 
I can guarantee you that ejecting a bullet from a die can be difficult, and a 
slight taper on the afterbody would greatly alleviate the problem. Figure 7- 6 
is a photograph of a 90 grain Hollow Point 270 bullet held between the paral- 
lel jaws of a dial gage micrometer. It can be seen that the afterbody starts 
tapering to a smaller diameter immediately in front of the base. Figure 7-7 
shows a photograph of a Remington 130 grain 270 Bronze Point that has a 
true cylindrical afterbody that is about 1 .2 calibers in length. Unfortunately, 
this bullet has a canelure groove, which reduces the length of the cylindrical 
afterbody. It also reduces the ballistic coefficient, and can cause bullet im- 
balance. It should be pointed out that 90 and 100 grain 270 bullets can’t have 
much more than a 1 .5 caliber cylindrical afterbody, otherwise the nose would 
be too blunt. Well, it is clear that if we fired the bullet shown in Figure 7-6, it 
could tip in the bore if it were fired from a smoothbore. However, the sides 
of the bullet are contacted by the rifling lands about 1 .5 calibers ahead of the 
base despite the tapered afterbody, which should help to stabilize the bullet 
and keep it from tipping. So, it seemed possible that the bullet might not 
actually cant in the bore, in spite of the fact that the afterbody is tapered. The 
only way that I could be sure that bullet cant was the cause of the asymmetri- 
cal muzzle blast problem, was to recover some bullets and examine them. 


Rifle Accuracy Facts 

Figure 7-6 - Photograph of a 90 grain 270 HP bullet held between the parallel 
jaws of a micrometer, showing the tapered afterbody. 

Figure 7-7 - Photograph of a Remington 130 grain 270 Bronze Point bullet held 
between the parallel jaws of a micrometer, showing the parallel sides of the 
cylindrical afterbody. 


Figure 7-8 - Photograph of a recovered 90 grain 270 HP bullet showing triangular 
shaped scuff marks on the side wall of the bullet between the rifling marks, which 
can be measured to determine bullet cant. 


Chapter 7: Muzzle Blast 

Bullet Recovery 

Recovering a bullet undamaged at high speed is tough to do, so I decided to 
cut the nose off (Figure 7-8). This increases the drag coefficient by a factor 
of 2.5 and helps slow it down. The calculated velocity at 300 yards was 1400 
fps. That was where I placed a 1.5 foot square by 4 foot long plywood box 
filled with pine sawdust. The 90 grain 270 HP bullets, which weighed 86 
grains after the nose was trimmed, traveled about 3.5 feet through the saw- 
dust and were recovered in good shape. This was farther than I had expected 
(2 feet), probably because the sawdust density (13 pounds per cubic foot) 
was less than I had expected (20 pounds per cubic foot). The 130 grain 
bullets went through the whole thing and were not recovered. If you want to 
recover the heavier bullets in less than four feet, drill out some of the lead in 
the nose to reduce the weight to less than 90 grains, use a longer box, or 
recover them at longer range. It may be a problem to adjust the sights at 
longer range to correct for the bullet drop. In this case it was 31 inches, 
which was precalculated and turned out to be correct. This weight can be 
scaled by the sectional density for other calibers. 

The angle of bullet cant can be determined from the recovered bullets 
by measuring the difference in length of the rifling marks from side to side. 
A simple equation can be derived that can be used to approximate the 
angle of cant. 

cant angle 28.65*L/Ro degrees 

L = differential length of rifling marks (inches) 

Ro = radius of the tangent ogive nose (1.2 to 1.5 inches) 

The recovered 90 grain bullets were measured and L was found to range 
between 1 0 and 20 mils. This meant that the cant angle ranged between 0.24 
and 0.48 degrees for an Ro of 1 .2 inches. This agrees well with the measured 
afterbody angle that was obtained from Figure 7-6. So the tapered afterbody 
can allow the bullet to cant in the bore by as much as 0.5 degrees. I found 
that the best way of measuring L was to measure the length of the scuff 
marks where the side of the bullet contacted the groove between the rifling 
lands. This scuff mark, which is roughly triangular in shape can be seen in 


Rifle Accuracy Facts 

Figure 7-8. It is difficult to photograph and is much more obvious to the eye. 
The triangular shape is due to the taper in the afterbody of the bullet. 

It is possible that this method of measuring bullet cant is in error by as much 
as a factor of two. The bullet may start out in the throat in the uncanted 
condition, causing the rifling marks to be even in length at first. The bullet 
may then cant further down the barrel, when maximum pressure is reached. 
This will lengthen the rifling marks on one side of the bullet, but cannot 
shorten the rifling marks on the other side. The same thing will happen to the 
scuff marks caused by the rifling grooves. Consequently, you can’t be sure 
that you have measured the maximum cant angle from recovered bullets, but 
I can’t think of any better way to do it. 

We now know that bullets can cant in the bore, which could be caused by a 
tapered afterbody. But, how much dispersion could this cause? 

Bullet Base Cant Dispersion 

In order to simulate the effect of bullet cant on dispersion I relied on an “Olde 
Engineers Trick”. Simply stated, it means that if you have a small error, that 
is difficult to measure, exaggerate the error so that it can be measured. For 
this approach to work you have to be careful not to change anything else. 
This can be done by cutting off the base of the bullet at a two degree angle 

Figure 7-9 - Bullet on left 
with base milled off at a 
2 degree angle compared 
with normal bullet on right. 
Small hole in the left side 
of the base of the 
modified bullet compen- 
sates for mass asymmetry 
caused by the slanted 
base. The bases of both 
bullets are resting on plate 
glass. Note that the 
modified bullet on the left 
leans toward the normal 
bullet on the right. 


Chapter 7: Muzzle Blast 

and then drilling a hole on the long side of the bullet to compensate for the 
shift in center of gravity (CG). This modification can be seen in Figure 7-9. 
The two degree base angle is about 4 times the maximum amount of bullet 
cant that I measured. It requires removing about 10 mils from the jacket base 
on the short side of the bullet. Since the jacket is only about 25 mils thick at 
the base, a 2 degree angle is about all the bullet can tolerate. A larger angle 
would result in thinning the base jacket so much that there would be a real 
risk of blowing the lead core through the jacket during firing. This could 
leave the jacket lodged in the bore, which is a very dangerous condition. It is 
also important to use a bullet with relatively sharp corners on the base, which 
minimizes the amount of material to be removed from the jacket at the base 
of the bullet. For this reason, 100 grain 270 soft point bullets were used in 
the experiment. The test routine is to fire four 3-shot groups with the base 
asymmetry pointed up, right, down, and to the left at muzzle exit. If you 
perform this test, it is necessary to remove the extractor and ejector from the 
bolt, and to use cases with at least 5 mils of headspace. Otherwise, the bolt 
will rotate the cartridge and mess up the experiment. The cases have to be 
ejected with a cleaning rod, so be sure to remove it before firing the next 
shot! It is a good idea to look down the bore just to be sure it is clear before 
inserting the next live round. The only way that I have found to index the 
cases in roll angle is to put a mark on the head of the case. The mark is 
rotated until it is properly indexed, and then the case is pushed all the way 
into the chamber with a finger. It isn’t easy but it can be done. This gives us 
four distinct groups spaced roughly 90 degrees apart, which tells us a lot 
about just how this base cant asymmetry works. The results of this test are 
shown in Figure 7-10. The mathematical centers of the groups are shown by 
squares, and the direction of the short side of the bullet is indicated. The 
bullet should be deflected in the direction of the short side of the bullet if 
there were no gyroscopic action. You can see that the groups are all rotated 
clockwise somewhere between 30 and 60 degrees. This means that the bullet 
was disturbed over the first 6 or more calibers of its travel after leaving the 
muzzle, which is to be expected. Schmidt and several coworkers at the US 
Army Ballistic Research Laboratory (Refs. 4 and 5) have shown that the bul- 
let is influenced by the muzzle blast for roughly 15 to 20 calibers. The stron- 
ger pressure, which has the biggest effect, is present much closer to the muzzle. 
Just why the group rotation is not more consistent is not known. However, 
there are other effects including the error in indexing the cartridges, bullet 
imbalance, statistical error in 3-shot groups, and other effects that could 


Rifle Accuracy Facts 

Figure 7-10 - Plot of the target showing the results of firing four 3-shot 270-groups 
with the slanted bases of the bullets indexed at 90 degree increments in roll angle. 
Square symbols indicate the center of each group. The radius of the inscribed circle 
(radius of dispersion) is 0.8 inches. 

easily explain the variation in rotation angle of the groups. The interesting 
finding is that a radius of dispersion of 0.8 inches resulted for a base cant 
angle of 2 degrees. This means that the maximum 0.5 degree bullet cant 
angle that we measured would result in group sizes approaching 0.4 inches if 
all other sources of error were eliminated. Even though this is a relatively 
crude experiment, I believe it shows that bullet cant causes dispersion. There- 
fore, bullet cant is a significant source of dispersion, even though it is smaller 
than some of the other error sources. 

After working on this problem for over a year I was able to run the same test 
in a rail gun chambered for the 6mm BR. The test was run in a tunnel range 
which eliminated wind effects. This equipment was mentioned in Chapter 4 
and described in detail in Appendix E and F. The results of the 6BR test with 
the bases of the bullets milled off at a 2 degree angle are shown in 
Figure 7-11. You can see that the results are similar to the results for the 270, 
except that the radius of dispersion is smaller (0.64 compared to 0.80). 


Chapter 7: Muzzle Blast 




Figure 7-11 - Plot of the target showing four 6mm BR groups fired with the bases 
cut off at a 2 degree angle and indexed at 90 degree intervals in roll angle. Radius 
of dispersion is 0.64 inches and is predicted by theory (solid circle symbols). 

The fact that the radius of dispersion was smaller indicated it might have 
something to do with the lower muzzle blast pressure of the 6BR. We will 
measure the effect of different powders on muzzle blast pressure later in 
this chapter. 

Canted Bullet Test 

Since the canted base test was only a test to see if there was a muzzle blast 
effect I decided to try testing the real case where the whole bullet is canted in 
the bore. The 6BR was tested by canting the bullets 0.215 degrees in the case 
neck and indexing them in roll just as before. The result was a group that 
looked like a four leaf clover and is shown in Figure 7-12. The radius of 
dispersion was 0.196 inches and is shown by the inscribed circle. The theo- 
retical value obtained from a trajectory simulation computer code was a little 
larger and was 0.243 inches. The 70 degrees clockwise rotation of the groups 
is predicted by the theory. There are at least two explanations why the experi- 
mental value was slightly smaller than the theoretical value. The bullet may 


Rifle Accuracy Facts 




1 - NOSE UP 






Figure 7-12 - Computer scan of the target where four groups of 4 bullets each that 
were canted 0.215 degrees in the case neck. The bullets were indexed in 90 degree 
intervals in roll. The radius of dispersion of 0. 196 inches is superimposed. The 
trajectory simulation predicted 0.243 inches for radius of dispersion. 

have straightened out slightly upon entering the throat or the Center of Grav- 
ity (CG) may have been slightly away from the side of the bullet most in 
contact with the bore. The bullet would only have to be pushed sideways 
about 0.05 mils to cause enough CG offset to explain the difference between 
the theory and experiment. Either one or both of these things are physically 
reasonable and may have happened. The important thing to realize is that 
only a 0.2 degree canted bullet angle resulted in a radius of dispersion of 
about 0.2 inches. This is a much larger effect than I would have expected 
from the canted base tests. You see, the radius of dispersion for the canted 
bullet tests was about 1 inch per degree of bullet cant while the radius of 
dispersion was only about 0.32 inches per degree of base cant. I would have 
expected the sensitivity to be about the same, but it wasn’t. One other thing 
that I noticed is that you have to back the canted bullets off the lands to obtain 
these results, otherwise the bullet misalignment will be reduced. The first 
time I tried the canted bullet experiment the bullets were in contact with the 
lands and the radius of dispersion was only 0. 15 inches. The test shown in 
Figure 7-12 had the bullets backed off the lands 30 mils. Most bench rest 
shooters push their bullets forward 10-20 mils into the lands. This may help 
reduce bullet canting in the case neck. The results of the canted bullet test 
indicate that 0.1 degrees of bullet cant will cause the bullet to be deflected 
roughly 0.1 inches at 100 yards. 


Chapter 7: Muzzle Blast 

Muzzle Blast Physics 

After working on the muzzle blast problem for over a year I still wasn’t con- 
vinced that I had it pinned down. I had theorized that bullet cant was causing 
the muzzle blast asymmetry that I had observed in the tuft screen experi- 
ment. Also, I had assumed that the muzzle blast asymmetry was pushing the 
bullet off course. I had shown that bullet cant does occur and demonstrated 
its effect on dispersion. However, I still wasn’t sure that bullet cant was caus- 
ing muzzle blast asymmetry. So, I decided to try to photograph the muzzle 
blast flow pattern using spark shadowgraphy. This technique gives you a 
shadow photograph of the muzzle blast flow. A complete description of the 
method is in Appendix G. But in brief you use a high energy (lOkv), short 
duration (0.4 microsecond) point spark light source that casts a shadow im- 
age either on a piece of fdm (12"xl8" lithograph film) or on a white screen. 
The image on the white screen can be photographed with Polaroid film. The 
light rays are absorbed by solid material (bullet, smoke) and distorted by 
density gradients such as shock waves. Some 1 00 Polaroid and about 40 
lithograph film exposures were made with the bullet at different distances 
from the muzzle. The flow region between the time the bullet exits the muzzle 
and outruns the blast wave is called the transitional ballistics region between 
internal and external ballistics. The shadowgraph studies were done with the 
rail gun chambered for the 6BR. 

Figure 7- 1 3 shows a picture of the precursor spherical shock wave formed by 
the compressed air and blow-by ahead of the bullet. The bullet is about three 
inches back down the bore. Figure 7- 1 4 (0 psec) shows the bullet just emerg- 
ing from the bore and the precursor shock wave is still ahead of the bullet. 
One p.sec (microsecond) is one millionth of a second. Figure 7-15(11 psec) 
shows the gas escaping behind the bullet when the base of the bullet is about 
one bullet length out of the muzzle. Figure 7-16 (56 psec) shows the bullet 
about 2.5 bullet lengths ( 1 2 calibers) from the muzzle and it is about halfway 
through what is called the Mach disk. If you look carefully you can see a dark 
vertical line near the base of the bullet. This is a normal shock wave caused 
by the fact that the gas flow is faster than the bullet (reverse flow). There are 
also shock waves emanating from the edges of the barrel caused by the ex- 
pansion of the jet and you can see a conical shock wave forming on the nose 
of the bullet. Figure 7-17 (90 psec) shows the bullet in the process of pen- 
etrating the main blast wave and just starting to penetrate the precursor shock 
wave. If you look at the upper part of the main blast wave you can see where 


Rifle Accuracy Facts 

Figure 7-13- 
photo showing the 
spherical precursor 
shock wave 
emerging from the 
bore. The precursor 
is formed by the 
compressed air 
and gas ahead of 
the bullet. The 
bullet is about 
three inches back 
in the bore. 

Figure 7-14 - 
showing the bullet 
just emerging 
from the muzzle 
at 0 psec. 

Figure 7-15 - 
showing the bullet 
base about one 
bullet length (0.86 
inches) from the 
muzzle. The 
spherical blast 
wave is beginning 
to form around the 
opaque cloud of 
smoke at about 
20 psec. The 
pressure on the 
base of the bullet 
is about 4000 psi. 


Chapter 7: Muzzle Blast 

Figure 7-16 - Shadowgraph showing bullet base about 2.5 bullet lengths ahead of 
the muzzle at 56 psec. By this time the pressure acting on the base of the bullet 
has dropped to a few hundred psi. You can see a normal shock wave from the 
reverse flow on the base of the bullet and bow shock on the tip of the bullet. 

Figure 7-17- Shadowgraph showing the bullet penetrating the main blast wave and 
starting to penetrate the precursor at 90 psec. The main blast wave is overtaking 
the precursor. The bullet is out of any significant effect from the muzzle jet. There are 
tiny unburned powder particles trying to penetrate the blast wave above the bullet. 


Rifle Accuracy Facts 

Figure 7-18 - Shadowgraph at 142 psec showing the bullet penetrating both the 
blast and precursor waves which have combined. There is a weak bow shock on 
the nose tip of the bullet. 

some unburned powder particles have just slightly penetrated the blast wave. 
In the last photograph, Figure 7-18 (142 psec), the bullet has penetrated the 
blast wave, which has combined with the precursor shock wave and the bul- 
let is leaving the effects of the muzzle blast. 

Now, some explanation is necessary. Originally I decided to do this experi- 
ment, even though it was time consuming (10 months) and expensive ($ 1 000), 
to see if I could see the asymmetry in the muzzle blast that I thought was 
there. Well, after examining over 100 images, most with canted base bullets, 
I could see no significant muzzle blast asymmetry like I had expected to 
see! While there were occasional minor distortions of the shock waves, there 
was no orderly, consistent data. This meant that the dispersion observed in 
the tests with both canted base bullets and canted bullets had to result from 
some cause other than muzzle blast asymmetry. When you think about it the 
difference in time between when the short side of the canted bullet leaves the 
muzzle and when the long side exits is only 0.2 psec. Not much can happen 
in that length of time. The other thing that happens is that spherical shock 
waves behave something like soap bubbles and they try to maintain a sym- 
metrical spherical shape. 


Chapter 7: Muzzle Blast 

So why did the tuft screen experiments indicate that there was muzzle blast 
asymmetry when we didn’t see it in the spark shadowgraphs? Well jets are 
unstable and perhaps the vortex that forms around the jet isn’t always sym- 
metrically located. Also, the vortex ring is similar to a smoke ring and can 
drift with the wind. At any rate the tuft screen studies, which got me in this 
mess in the first place were misleading. The only thing I could think of was 
to try to analyze the observed bullet cant and canted base dispersion data 
using the 6DOF trajectory simulation computer code (see Chapter 10) to see 
if that would tell us what causes the dispersion. 

Theoretical Analysis 

Figure 7-19 shows a sketch of the two ways that testing was done. Figure 7- 
19(A) shows the canted base test and Figure 7- 19(B) shows the situation 
where the whole bullet is canted (i.e., the real case). In the canted base situ- 
ation a force vector resulting from the muzzle blast pressure acting on the 
base is drawn perpendicular to the base. Pressure can only act perpendicular 
to a surface. This force is under the CG of the bullet producing a moment in 
the nose up direction. Later we measure the muzzle blast pressure (5000 psi 
for the 6BR) so we can calculate the force. From some other data that I had 

Figure 7-19 - Drawing showing the physical model of the effect of muzzle blast on a 
bullet with canted base and a canted bullet. When implemented in a 6DOF 
trajectory simulation computer code the experimental radius of dispersion is 
correctly predicted. 


Rifle Accuracy Facts 

(Reference 4 and 20) it was clear that once the base of the bullet went through 
the Mach disk, the pressure on the base of the bullet was very small and 
could be ignored. From the spark shadowgraphs we can determine the time 
between when the bullet first emerges and penetrates the Mach disk to be 
about 50 psec (8 calibers). Now we know that the muzzle blast pressure 
drops from 5000 psi to about 150 psi in 50 psec for the 6BR but we don’t 
know just how the pressure drops off. I had some other data that indicated 
that the pressure drop was an exponential decay and that assumption was 
used in the 6DOF computer simulation program. When I ran the computer 
program it indicated that the radius of dispersion for the 6BR should be about 
0.64 inches. If you compare that with Figure 7-11 you can see that the theory 
agrees with the experimental value of 0.64 inches. I ran the same calculation 
for the 270 using the measured muzzle blast pressure of 1 1 ,500 psi and got 
0.85 inches for the radius of dispersion. You can see that the value for the 
radius of dispersion for the 270 in Figure 7-10 was 0.8 inches, so the theory 
agrees well with both the 270 and the 6mm experimental data. 

Well, I think we now understand the effect of muzzle blast pressure on canted 
bullets. Some degree of in-bore bullet cant may always occur. Factors that 
effect bullet cant are a tapered bullet afterbody, the length of the cylindrical 
afterbody, and how well the bullet is centered with respect to the bore axis 
before firing. Factors that effect how perfectly the bullet is centered with 
respect to the bore axis are the amount of case neck run out, the amount of 
bullet run out in the loaded round, how well the chamber axis is aligned with 
the bore axis, the degree of throat asymmetry, and the bullet seating depth 
into the lands. It is also possible that the base of the bullet is not always 
perpendicular to the centerline of the bullet. 

So, how do we minimize the error caused by muzzle blast pressure? 

Resized Bullets 

I first stumbled onto this trick of resizing commercial bullets purely by acci- 
dent in the late 60’s. I had a Remington 721 chambered for the 300 Weatherby 
that shot 5-shot groups of 2.5 inches at 300 yards. I then built a similar rifle 
chambered for a 270 Magnum using the 270 Wby case with a straight shoul- 
der which only shot 3.5 inch groups at 300 yards. I had some theories at the 
time as to why the 300 shot smaller groups than the 270 that led me to try 


Chapter 7: Muzzle Blast 

Figure 7-20 - Photograph of a 90 grain 270 HP bullet resized from 0.2770 to 0.2765 
inches in diameter held between the parallel jaws of a micrometer. Comparison with 
Figure 7-6 shows how resizing the bullet increased the cylindrical afterbody length. 

resizing the 270 bullets. I tried resizing the 270 bullets by 0.3, 0.5, and 0.7 
mils. I found that the bullets resized by 0.5 and 0.7 mils reduced the size of 
the 300 yard groups from 3.5 inches down to 2.5 inches. Well, it has only 
recently dawned on me that what was really happening was the effect of 
muzzle blast pressure on bullet cant. Resizing the 270 bullet had reduced 
bullet cant. You see, I was using 1 80 grain Remington Bronze Points in the 
300 Mag, which had long cylindrical afterbodies, and I was using 150 grain 
SP bullets in the 270 Mag, which had tapered afterbodies. 

The effect on the length of the cylindrical afterbody of slightly resizing a 
bullet can be seen in Figure 7-20 which shows a resized 90 grain HP held in 
a micrometer. Comparison with Figure 7-6 will show how resizing has length- 
ened the cylindrical afterbody. I also recovered some fired resized 90 grain 
HP bullets that showed no evidence of canting. Recall that the recovered 
regular 90 grain 270 HP bullets did show evidence of canting. 

I tried resizing 6mm match bullets but it didn’t help. All of the 6mm match 
bullets from three different custom bullet makers that I checked had a thing 
called a pressure ring at the base of the bullet. Right at the heel of the bullet 
there is a narrow ring that varies from 0.3 to 0.6 mils over groove diameter, 
depending on the source. I couldn’t understand whether this condition re- 
sulted from someone’s creative idea or was an artifact of production. So, I 
called Walt Berger and he said it was an artifact of production and no one 


Rifle Accuracy Facts 

seemed to know how it happens. However, the bullets shoot well so they 
don’t try to change it. Incidentally, my handmade 270 flat base bullets don’t 
have this pressure ring so I think it has to do with the relationship between 
the core swaging die and pointing die diameters. Some folks believe that the 
pressure ring provides a better gas seal, and maybe it does. However, I no- 
ticed that it is comparatively easy to push the point of the bullet off center 
because the case neck only grips the rear end of the bullet. I don’t know 
whether this is good or bad. This pressure ring may make it easier for the 
bullet to line up with the throat. 

Case Neck Asymmetry 

I had hoped to avoid getting into the case neck asymmetry problem, even 
though bench rest shooters go to great lengths to correct it. The goal is to 
have the bullet enter the throat perfectly aligned and exactly on center with 
the bore. Otherwise, the bullet may cant while entering the throat. If you 
check the run out of the bullet axis with respect to the case axis on factory 
ammunition you will observe as much as 6 mils eccentricity (total indicated 
run out, TIR), which is a lot. You can also measure as much as ± 1 mil varia- 
tion in neck thickness around the periphery of the neck, although the varia- 
tion is usually more like ±0.5 mil. The 270 chamber in the experimental rifle 
has a neck diameter of 0.307 and a loaded cartridge has a neck diameter of 
between 0.303 and 0.306, depending on the brand of the case. Case neck 
average thickness varies between 13.0 and 14.5 mils between brands. This 
means that the outside of the case neck can be off center by as much as 2 
mils. If you add the 1 mil variation in neck thickness, it is possible for the 
base of the bullet to be at least 3 mils off center. Now even if the bullet is 
seated well forward into the lands the bullet can be canted by as much as 0.5 
degrees. Similar results were obtained on the 6mm Remington. Consequently, 
case neck asymmetry may have more to do with bullet in-bore canting than 
the shape of the bullet, and if one is really striving for good accuracy some- 
thing has to be done to correct this situation. 

At first I tried to realign the outside surface of the neck by making a two 
piece die. It held the case body and shoulder in one piece and the neck in a 
separate piece. The die was spun in the lathe while a ball bearing tool was 
pressed against the neck portion. This approach did not work at all, even 


Chapter 7: Muzzle Blast 

when the necks of the cases were annealed. Then I dial gaged the necks of a 
number of fired cases and found that the outside surface of the necks ran true. 
This was encouraging, since I now had something that was concentric to start 
with! The next thing I did was to machine the inside of the necks removing 
just enough to end up with a uniform neck thickness. The shell holder which 
held the case in the lathe collet was made by cutting a chamber in a piece of 
bar stock. This was then held on the chambering reamer while the outside of 
the die was turned to the exact internal dimension of a 3/4 inch lathe collet. 
Next, an ordinary inside boring tool was used with a light cut at high speed to 
machine the inside of the case neck while the case was held in the die. With 
Remington and Norma 270 cases the neck thickness ended up being about 13 
mils, which means the average neck thickness was reduced by about 1 mil. 
The next step was to neck resize the case just enough to hold the bullet, and 
hope that the inside of the neck would remain on center. Well it worked 
much better than I had expected. Roughly 40% of the cases had essentially 
zero bullet run out when loaded, about 40% around 0.5 mil and 20% in the 
vicinity of 1 mil or less. This is a vast improvement over ordinary ammuni- 
tion. Unfortunately, I don’t know of any way of doing this without the proper 
equipment. The neck resizing die was made by grinding out the body of the 
die so that the body of a fired case would just fit into the die. The neck 
resizing portion was opened up with emery paper from 0.299 to 0.302. In 
this way the die is perfectly concentric with the lathe spindle. Bench rest 
shooters use rifles that have undersize chamber necks and the case necks 
must be turned down before loaded rounds will chamber. The case neck is 
turned down so that the final neck wall thickness is about 8.5 mils and the 
variation in thickness is kept to less than 0.1 mil from case to case. The 
radial clearance between the neck of a loaded round and the chamber neck is 
usually only 0.4 to 0.7 mils. The advantage to the bench rest approach is that 
the neck need only be very slightly resized. The disadvantage is that toler- 
ances must be very carefully controlled and only modified ammunition can 
be used. 

Later on I found a better way of reducing the bullet run out, that may be a 
better long term solution. First, I machined the inside of the neck of a fired 
case to obtain a uniform wall thickness just like before. Then I used an old 
rifling head to cut six straight rifling grooves in the neck portion of the neck 
resizing die. The depth of the rifling cuts were adjusted so that the neck of a 
resized case would be close to the inside diameter of the chamber neck. The 


Rifle Accuracy Facts 

Figure 7-21 - Cross section 
view of barrel showing 
how the splined neck 
cartridge case 
keeps the bullet 
centered in the 
bore. The 
splined neck 
case is made 
by first 

machining the 
inside of the 
neck of a fired 
case to obtain 
a uniform neck 
thickness, then 
resizing in a die 
made by making 
rifling cuts in the 
neck portion of the die 



case necks are then resized in this die, and the result is a case neck that has a 
splined appearance. A cross section view of the chamber, case neck and 
bullet is shown in Figure 7-21. The radial clearance between the case neck 
and chamber neck is only a few tenths of a mil. You can see that the bullet 
has to end up on the center of the bore, because there isn’t any place else 
for it to go, if both the outside and inside of the case neck is concentric with 
the bore. When I checked the run out of the bullets in loaded ammunition, 
most of the bullets were within a few tenths of a mil with the worst case 
being about 2 mils, which is a big improvement over doing nothing. Now 
I realize that everybody doesn’t have a precision lathe with collets and a 
rifling head lying around. However I feel sure that the manufacturers can 
come up with a cheaper way to do this work. After all, they make special 
equipment now for bench rest shooters. One advantage of this method is 
that you don’t have to worry about getting a close fit between the chamber 
and case neck like you do with the traditional bench rest method. You can 
also work with a standard chamber such as the one in the experimental rifle. 
However, you would have to seal the tiny gap between the bullet and the 
inside of the neck to prevent moisture from entering the case, if you are going 
to store loaded ammunition for an extended period of time. Some people 
may worry about gas passing through this annular gap. I don’t think it’s a 
problem because only a very small amount of gas can travel through such 


Chapter 7: Muzzle Blast 

a small radial gap .e. 1 .5 to 2 mils). In fact it may prove to be an improve- 
ment because it may blow out the burned powder residue between shots. 

Just how close this bullet centering with respect to the bore centerline has to 
be held is not clear. However we know that bench rest rifles won’t shoot well 
without modifying selected cases. This may mean that it is necessary to hold 
the bullet on center within 0.5 mil or less. Anyway it is time to test fire the 
experimental rifle with resized bullets and the splined neck cases and see if 
we can see any improvement. You may recall from Table 4 back in Chapter 4 
that the average dispersion was 0.884 inches. The results of this test are 
shown in Table 8. 



Resized 90 grain 270 HP bullets 
with splined case necks. 

Extreme Spread for eight 5-shot groups at 100 yards 

Average Maximum Minimum 

0.804 1.399 0.386 

Well, as you can see from Table 8 the average dispersion dropped from 0.884 
to 0.804. We can use the method of Root Mean Squares (RMS) to evaluate 
the effect of the resized bullets, which is 

error = (0.884 2 - 0.804 2 ) l/2 = 0.367 inches. 

This calculated error agrees well with the estimated error from the previous 
experimental measurements (0.2 to 0.4 inches). If we make the same RMS 
calculation on the 300 (2.5 in.) and 270 Mag (3.5 in.) results at 300 yards, 
that was mentioned earlier, we get an error contribution of 0.81 inch at 100 
yards on the magnums. This error is roughly twice that obtained on the 270 
Winchester cartridge. This doesn’t surprise me, because the muzzle blast 
pressure on a magnum is 1 .5 to 2 times that of a standard case 270. At any 
rate, I think that the problem of muzzle blast pressure acting on canted bul- 
lets can be solved to some extent by using bullets with a cylindrical afterbody 
of sufficient length and using cases with concentric or spline case necks. 


Rifle Accuracy Facts 

The 270 Winchester did improve some, but not as much as I had expected. 
Also, with this method of modifying the case necks it appeared that resizing 
the bullet had little effect, which might be expected. However, the 6mm Rem 
bench gun accuracy improved dramatically with the splined neck resizing 
shown in Figure 7-21. It started shooting groups with 6mm match bullets 
that averaged around 0.25 inches with a 14" twist barrel compared to one 
inch groups with the old 10" twist barrel. This led me to suspect that some- 
thing was wrong with the bullets, and it turned out to be due to bullet core 
failure. We investigate bullet core problems in the next chapter (Chapter 8). 

Muzzle Blast Pressure Reduction 

The fact that a fast burning powder will result in a lower pressure at the 
muzzle than a slow burning powder was mentioned earlier. However, for the 
same muzzle velocity the faster burning powder will produce a higher cham- 
ber pressure. Nothing ever comes free in this business! I decided to test this 
contention by measuring the in-bore pressure at the muzzle using the strain 
gage method that we used to measure chamber pressure back in Chapter 2. 
Since we are only interested in the comparison of muzzle pressures resulting 
from the two different powders, we don’t have to go through the tedious 
calibration procedure used in measuring chamber pressure, and the theoreti- 
cal calibration will suffice. We will use 49 grains of IMR 4064 and 57 grains 
of IMR 4831 for the test, which yield approximately the same peak chamber 
pressure. The 90 grain 270 hollow point bullet was used with both powders. 
The test results (Figures 7-22 and 7-23) showed that the muzzle pressure was 
1 1,500 psi for IMR 4831 and 7,100 psi for IMR 4064, which means that the 
muzzle pressure was about 38% less for the faster burning IMR 4064 pow- 
der. The muzzle velocity for the IMR 4064 was about 150 fps less than that 
of the IMR 4831. The negative blip on the oscilloscope data is probably 
caused by a compression wave that runs a few inches ahead of the barrel 
expansion caused by the internal pressure behind the bullet. The base of the 
bullet passes under the strain gage at about 1 .37 msec where the peak pres- 
sure occurs, and the base of the bullet exits at about 1 .40 msec. Notice that 
the muzzle pressure of 1 1,500 psi agrees well with the pressure on the base 
of the bullet at the point of muzzle exit shown in Figure 2-21. So now we 
know that the choice of powder significantly effects the magnitude of the 
muzzle blast pressure. 


Chapter 7: Muzzle Blast 


Figure 7-22 - Measurement of the muzzle pressure near the muzzle of the barrel 
for IMR4831 powder. 

Figure 7-23 - Measurement of the muzzle pressure near the muzzle of the barrel 
for IMR4064 powder. 

Before leaving this fast and slow burning powder discussion, we should point 
out that the major difference between these two single base powders is in 
grain size. The grain diameter of IMR 4064 is 0.032 inches and the grain 
diameter of IMR 4831 is 0.041 inches. This means that IMR 4064 will burn 


Rifle Accuracy Facts 

out about 28% faster than IMR 4831 if the burning rate is the same for the 
two powders. This means that the peak chamber pressure will occur at about 
0.47 msec for IMR 4064 compared to 0.65 msec for IMR 483 1 (see Figure 2- 
21, Chapter 2). I am told that all IMR powders are single base powders, 
which means that their burning rates are similar, and the main difference is in 
grain size. The burning rates of all single base gun powders are roughly the 
same, regardless of whether you are working with rifle powder or 8 inch 
cannon powder. The burning rate can also be modified by the addition of 
inhibitors. We can observe the effect of grain size in Table 9, where the grain 
diameter and web thickness is shown for several powders that range from 
slow to fast burning. 


Powder Grain Diameter 




Grain Diameter (inch) 

Web Thickness 

H 570 



H 4831 



IMR 4831 



IMR 4350 



IMR 4320 



IMR 4064 



IMR 3031 



H 322 


IMR 4198 



This table demonstrates the large difference in grain diameter and web thick- 
ness between fast and slow burning powders. The data were obtained by 
actually measuring the grain diameter with a micrometer, and are slightly 
different from Du Pont published data in a few instances. Consequently, when 
we talk about fast and slow burning powders, we are generally talking about 
fine and coarse grained powders, and the time it takes for the grain to burn. 


Chapter 7: Muzzle Blast 






$ 10,000 





[jj 5,000 




0 0.01 0.02 0.03 0.04 


Figure 7-24 - Graph showing how powder grain diameter effects muzzle pressure. 
The larger grain slow burning powders produce a higher pressure at the muzzle 
than smaller grain faster burning powders. 

The two experimental muzzle pressure points for the 270 (open circle sym- 
bols) are plotted in Figure 7-24, and a curve faired through them. This al- 
lows one to graphically see the effect of grain size on muzzle pressure. For 
instance, changing from IMR 4831 to IMR 3031 powder will reduce the 
muzzle pressure by nearly a factor of two. 

So now let’s talk about the other data points on Figure 7-24. The square data 
points are from the 6mm Remington in the rail gun. You can see that the 
muzzle pressure for the 270 Winchester and 6mm Remington both with 24" 
barrels is practically identical for IMR4831. It should be, because the ratio 
of case capacity to bore area is about the same. The next thing to notice is 
that the muzzle pressure for the 6mm Remington with a 28" barrel is about 
9,000 psi. This pressure is about 4,000 psi less than it is on the 6mm 
Remington with a 24" barrel. 

Now notice the black square at about 5,000 psi which is the muzzle pressure 
for the 6mm Remington with a 27" barrel that has a ventilated muzzle (see 

<3> g tn 


2 12 2 i 






□ 24" BARREL 
d 28" BARREL 










6mm PPC 


• 21" BARREL 

* 24" EST. .....f*" 



Rifle Accuracy Facts 

Figure 7-25). The 
muzzle is venti- 
lated with twenty 
four 0.078" diam- 
eter holes in the 
bottom of the ri- 
fling groove. The 
rifling lands are 
uninterrupted and 
continue to sup- 
port the bullet un- 
til muzzle exit. 

The larger outside 
holes are 3/16"D 
drilled within 

0.15" of the rifling groove. This allows insertion of a 5/64"D milling cutter 
with a 3/16" shank to cut the final 0.15 inches. A milling cutter was used to 
cut the holes to minimize the formation of burrs. The inside sharp edges of 
the vent holes burn off after a number of rounds are fired (perhaps 50) and 
they do not disturb the bullets. By the way the groove is 0.093" wide so the 
hole is slightly smaller than the groove. The bullet is constrained by the 
lands until it exits the muzzle and the pressure at the muzzle is much re- 
duced. Do not confuse this method of muzzle venting with the usual recoil 
reducer. The usual recoil reducer uses a counter bore with a diameter greater 
than the bullet diameter. In this case the holes do not have to be precisely 
located in the groove. However, the bullet is upset the instant it leaves the 
constraint of the lands and even though the muzzle pressure is reduced it 
can’t reduce the effect of muzzle blast pressure on the bullet exit dispersion. 

I was also able to measure muzzle pressure on a custom 6mm PPC Light 
Varmint (LV) bench rest gun owned by a friend of mine (Dr. Jack Jackson). 
This gun had a 21" barrel which seems to be typical of bench rest rifles and 
the data is shown by the black circle symbol. The load was a fairly hot load 
of H322 (27.8 grains), which is a fast burning powder. Consequently, the 
peak chamber pressure is probably in the vicinity of 60,000 psi instead of the 
53,000 psi chamber pressure for the 270 and 6mm Remington. Therefore the 
muzzle blast pressure on the 6PPC would be expected to be correspondingly 
higher. When one corrects the data for a 24" barrel length (flagged black 

Figure 7-25 - Photograph of the ventilated muzzle. 

Chapter 7: Muzzle Blast 

circle symbol), you can see that the muzzle blast pressure is close to the 
normalized curve. So you see that powder burning rate (grain diameter), peak 
chamber pressure, and barrel length all effect the muzzle blast pressure. Even 
so, the 6PPC has a low muzzle pressure by virtue of its small case capacity, 
which allows the use of fast burning powders with a full case load. 

Well OK, did the muzzle ventilation help? It did. It reduced the average 5- 
shot 100 yard group size from about 0.35" to 0.23" with match bullets and a 
14" twist in the 6mm Remington rail gun. This is not as good as a top flight 
6PPC HV gun or the 6BR rail gun which average in the high ones (i.e., 0.18"). 
The ventilated muzzle might be a good idea on sporters and long range mag- 
num rifles, but there is talk about outlawing it in Hunter Class bench rest 
competition because of the increased muzzle blast on nearby shooters. I 
personally can’t tell if it makes much difference. 

The vented muzzle was sectioned and the sharp corners at the vent holes had 
been rounded on the downstream corner of the holes by the hot gasses. Also 
there were copper smears just downstream of the vent holes. Just how im- 
portant this is I don’t know, but it can’t be good. This type of muzzle venting 
is not a trivial machining job and would be expensive to do. Indexing the 
vent holes so that they end up in the grooves is difficult. 

What this all amounts to is that the effect of muzzle blast pressure on group 
size can be decreased by reducing the muzzle blast pressure. The muzzle 
blast pressure can be reduced by using a smaller grain or faster burning pow- 
der, longer barrels, lower chamber pressure, or a muzzle ventilator. How- 
ever, for a given case volume you have to give up velocity, or bullet weight, 
or increase the maximum chamber pressure to obtain the same velocity. This 
usually means that one has to use a lighter load with the faster burning pow- 
der that won’t fill the case, which may result in greater shot-to-shot velocity 

The bench rest shooters optimized this problem by going to the 6 mm PPC 
which has a much smaller case than the regular 6 mm Remington, and using 
powders that are as fast or faster than IMR 4198 with 60-70 grain bullets. 
Consequently, the muzzle blast pressure effect is greatly reduced. Unfortu- 
nately, while this works well at moderate ranges, the light bullets with low 
sectional densities don’t do well at long (600-1000 yard) ranges. So, at long 
ranges the only thing that can be done is to use heavy bullets and larger 


Rifle Accuracy Facts 

capacity cases with slow burning powder. These heavy long range target 
guns usually have long (30 inch) barrels that reduce the muzzle blast pres- 
sure to some extent. 

The 270 Winchester cartridge that we are working with is a medium capacity 
case that is filled with IMR 4831 or IMR 4350. These powders provide 
optimum velocities, but also give high muzzle blast pressures. The solution 
is to use slow burning powders with heavy bullets ( 1 30 grain) for hunting and 
to switch to a faster burning powder and light bullets (90-100 grain) for tar- 
get shooting. 

Muzzle Crowning 

Just how one shapes or crowns the muzzle of a barrel for best results has been 
the subject of an endless series of articles in print over the years. As far as I 
can see most of this stuff has been pure drivel (unadulterated by any facts). I 
think the only fact that we have to go on is that nobody really knows, includ- 
ing this author. As far as I can tell it doesn’t really matter, as long as the 
crown is symmetrical and perpendicular to the bore. I’ve tried all of the most 
common shapes (Figure 7-26), and I can’t tell any difference between them. 
The circular or sporter crown, which is used on most commercial guns, looks 
nice and does a good job of protecting the end of the rifling. However, it is 
more difficult to machine and keep centered than the two other types of crowns 
shown in Figure 7-26. The bench rest flat crown is the easiest to machine and 
least sensitive to just how well the bore is centered. It may be slightly in- 
dented near the bore to protect the rifling, although I just use a flat crown 
without the indentation on target rifles. Many custom bench rest barrels have 
the 1 1 degree conical crown. Why this should be any better, I don’t know. 
However, the 1 1 degree angle probably came from the fact that tapered 
afterbodies (such as boat tails on bullets) will suffer from flow separation if 
the cone angle is greater than 1 1 degrees. This has nothing to do with jet 
flow. Someone probably saw this information and incorrectly assumed that 
it would apply to muzzle jet flow. But the conical crown is probably as good 
as any, and maybe they know something I don’t. The bottom line is that 
nobody really knows what crown shape is best, or even why it might be best. 
Consequently, you might as well use whatever crown that you like, as long as 
it is symmetrical with the bore axis. 


Chapter 7: Muzzle Blast 




Figure 7-26 - Various techniques of crowning gun muzzles. 


By using the tuft screen we found that the muzzle blast appeared to be asym- 
metric. We found by inspection that most bullets do not have a cylindrical 
afterbody of sufficient length to prevent the bullet from canting in the bore. 
Bullets were recovered which showed canting, even though the measure- 
ment accuracy was less than desired. The measurements taken on the re- 
covered bullets indicated a cant angle of 0.25-0.5 degrees. 

Bullets were then modified by slicing off the base at a two degree angle and 
these bullets were then fired in four groups with the canted bases indexed 
every 90 degrees. The result showed that a two degree base cant produced a 
radius of dispersion of 0.8 inches for the 270 and 0.64 for the 6mm BR at 
100 yards. Later a computer code was developed which accurately pre- 
dicted the test results. 

We then took spark shadowgraph pictures of the flow field in an effort to 
detect asymmetries in the muzzle gas flow. Much to my surprise, no 


Rifle Accuracy Facts 

significant flow asymmetry was observed. This observation led to the devel- 
opment of a computer code that accurately predicted the canted base target 
results for both the 270 and 6mm bullets. Firing tests were then conducted 
with the bullet canted in the case neck at an angle of 0.215 degrees. These 
tests showed a radius of dispersion of 0. 1 96 inches at 1 00 yards and the com- 
puter code predicted a radius of dispersion of 0.243 inches. Since 0.2 de- 
grees of bullet cant can easily happen, the dispersion from canted bullets can 
be large. 

We then explored methods of reducing bullet cant. The 270 bullets resized in 
diameter by 0.5 mils, that were recovered, demonstrated much less in-bore 
bullet cant. Resized bullets reduced the average group size from 0.884 to 
0.804 inches at 100 yards in the 270, indicating that bullet in-bore cant was 
corrected to some extent by resizing. Resizing 6mm match bullets had no 
effect on group size in the 6BR. The fact that resizing the 6mm match bullets 
had no effect was likely caused by the case neck machining combined with 
seating the bullets into the lands which helps prevent significant bullet cant- 
ing. The bullets were found to be off center in unmodified 270 and 6mm 
Remington cases and this was corrected by machining the inside of the case 
necks, and using a special spline crimp. The spline crimp greatly improved 
the accuracy of the 6mm Remington with Cook match bullets, but only had a 
small effect on the 270. At this point it became obvious that something was 
wrong with the 90 grain 270 bullets that were being used, and we investigate 
this in the next chapter. 

The muzzle blast pressure was measured using strain gages and it was deter- 
mined that large cases (270 Win.) with relatively slow burning, large grained 
powder had a much larger muzzle blast pressure than relatively fast burning 
small grained powder. Muzzle blast pressure was also decreased with longer 
barrels and ventilated muzzles. Muzzle ventilation was tried and it did re- 
duce the muzzle blast pressure as expected and produced a significant reduc- 
tion in group size. However, the type of muzzle venting that was used is a 
difficult machining job that would be expensive to do in production. 


T he lead core in a jacketed bullet is subjected to a large shearing stress at 
the interface between the jacket and the core during spin-up. As the 
bullet enters the rifling a large angular acceleration occurs which spins up the 
jacket. The lead core is heavy and has a large spin moment of inertia that 
resists this large angular acceleration. The core is driven by friction forces 
between the core and the jacket and shear stresses developed by the internal 
indentations in the jacket caused by the rifling engraving. These internal 
indentations protrude into the core about two mils. If the lead core is too 
weak to stand this shearing stress, core stripping results and the core will 
have a slower spin rate than the jacket when the bullet exits the muzzle. The 
maximum differential spin rate that I measured (5.5%) results in the core roll 
angle lagging behind the jacket roll angle by as much as 20 degrees. After 
muzzle exit the core slows down the jacket spin rate and the jacket speeds up 
the core spin rate slightly until both the core and jacket are at the same spin 
rate. The resulting spin rate of the bullet is slower than it would have been if 
core stripping had not occurred. Just how this effects the bullet’s trajectory is 
not known. However, it probably results in a center of gravity (CG) asymme- 
try and certainly produces a slower, variable spin rate. We can, and will 
measure the variation in spin rate, but I don’t know of any way to measure the 
effect of core stripping on CG asymmetry. We start out by determining core 
hardness as a measure of the shearing strength of the lead cores in several 
bullets. We also measure the torque required to strip the core in various 
bullets. This will tell us how likely it is for core stripping to occur. 


Rifle Accuracy Facts 

Figure 8-1 - Photograph of the Brinell Hardness Tester. 

Laboratory Core Stripping Tests 

The first thing that was done was to make a Brinell Hardness Number (BHN) 
test device which is shown in Figure 8-1, because I couldn’t find a local 
laboratory that had one. The BHN test device is nothing more than a spring 
loaded plunger that screws into a loading press and applies a known load on 
a small (3/16" diameter) ball bearing, which creates a small crater in the lead 
sample. If the load, ball diameter, and crater diameter are known, the BHN 
can be determined from the following equation. 

BHN = 0.0004485*F/{(7t/2)*D 2 *[l-V(l-(d/D) 2 ]} 


F = load, pounds (100 typical) 

D = ball diameter, inches (0.1875) 
d = diameter of crater in sample, inches 
71 = 3.14159 

According to engineering handbooks and the experimental stress tests that I 
ran in my hydraulic press on several samples, the core yield stress, or strength 
of the core can be determined by multiplying the BHN by 5 1 5. The results of 
these hardness tests for bullets from four different manufacturers are shown 
in Figure 8-2. The data for pure lead and Linotype metal are included for 
comparison. You can see that the measured core hardness and strength varies 
a lot between bullets — much more than I would have expected. I chose these 
bullets to work with because I had reason to believe from test firings that the 
65 grain 6mm match bullet never strips at a moderate load in a 10 inch twist, 
that the 270 90 grain HP bullet is marginal in a 10 inch twist, and that the 68 
grain match bullet always strips in a 10 inch twist. Now before anyone gets 
excited I want to point out that the 6mm 68 grain match bullets perform very 
well in bench rest rifles with a 14 inch twist, where they are intended to be 
used. So, we can see that the core hardness and strength results are in quali- 
tative agreement with the firing test results. So, what does this prove? 


Chapter 8: Bullet Core Problems 


Figure 8-2 - Measured core Brinell hardness and core yield stress (strength) for the 
cores of four test bullets. Pure lead and linotype metal are added for reference. 

It proves that the 65 grain match bullets have the strongest core material in 
the lots of bullets tested. However, it doesn’t tell us how much torque it takes 
to strip a core. To find out, we will have to measure it. 

Figure 8-3 shows a torque wrench designed to measure the core failure torque. 
A blade similar to a screw driver extends down into the lead core from the 
end of the torque wrench. The blade of the wrench is inserted into the nose 
of a bullet that has been swaged into a short section of barrel. The top l/8th 
inch diameter rod serves as a pointer and the bottom rod serves as a flexure, 
and is used to apply a torque to the driver blade. The torque required to cause 
core failure is read on a calibrated card attached to the flexure rod. The 
assembly is held in a vise with the pointed end up. A downward compression 
load of about 1000 pounds is applied to the pointed end, which partially 
simulates the set back load. The top of the device is pointed to reduce the 
friction torque between the top of the wrench and the press that is applying 
the simulated setback load. A 3/16 inch diameter flexure rod was used in 
testing 270 bullets. The results of the core failure torque are shown in Figure 
8-4 for room temperature (70 °F) and at an elevated temperature of 250 °F. 


Rifle Accuracy Facts 


Now I don’t know for sure just 
how hot a sporter bore gets. I 
know that the bore gets above 200 
°F on a hot day after firing sev- 
eral shots, because water boils 
when I pour it into the barrel to 
cool it off. Also, bore surface 
temperatures of 1000 °F of short 
duration have been measured by 
the Army (Reference 3). As you 
can see, temperature makes a big 
difference, and I suspect that this 
is one of the reasons why hot bar- 
rels usually don’t shoot very well. 

I have measured chamber tem- 
peratures of 133 °F on a cool day 

after firing 15 rounds, and I would expect the throat temperatures to be sig- 
nificantly higher. I don’t know how hot the bullet gets sitting there in the 
throat for a while, but it must be over 133 °F on a hot day after one fires 
several rounds. Also shown on Figure 8-4 (dashed lines) is the estimated 

Figure 8-3 - Photograph of the torque 
wrench used to measure the core failure 
torque on four test bullets. 

Figure 8-4 - Core failure torque for the four test bullets at normal and 
elevated temperatures. 


Chapter 8: Bullet Core Problems 

spin-up driving torque for the 270 with a 10 inch twist and for the 6mm with 
either a 10 or a 14 inch twist. You can see that the 65 grain match bullet core 
should survive spin-up while the 68 grain match and the 90 grain 270 bullets 
should be either marginal or fail in a 10 inch twist. The 68 grain 6mm bullets 
should survive a 14 inch twist and the experimental data shows that it does. 
The estimated spin-up torque was obtained by first computing the equilib- 
rium driving torque from the peak chamber pressure, which can be done very 
accurately, and then multiplying the equilibrium driving torque value by a 
factor of two to account for the fact that the spin-up torque is a dynamic 
rather than a static load. The equilibrium angular acceleration is 

a = (P*A*g*2*7t)/(W*Tw), rad/sec 2 


P = peak chamber pressure, psi 
A = bore cross-section area, in 2 
W = bullet weight, pounds, (grains/7000) 

Tw = twist, inches/12 

g = gravitational acceleration, 32.2 ft/sec 2 


The equilibrium driving torque is obtained by multiplying the angular accel- 
eration by the core spin moment of inertia. 

Te = a * lx * 12, inch-pounds 
where the spin moment of inertia is 
lx = 1/2 * m * r 2 , slug-ft 2 

m = core mass = (core weight in pounds) / g 
r = core radius, ft 

The dynamic driving torque (effective spin-up torque) is then obtained by 
multiplying the equilibrium driving torque by a factor of two. Now, while I 
know from experience that the dynamic factor of two is quite reasonable for 
this case, I am unable to quote restricted references, so you will just have to 
take my word for it. Also note that the spin-up torque is directly proportional 
to peak chamber pressure. Also, the spin-up torque is, to some extent, a 
function of the amount of bullet free run before striking the rifling. In this 
case the free run is short enough that the factor of two is valid. Consequently, 


Rifle Accuracy Facts 

our core failure torque measurements and estimated spin up torque bound- 
aries should be reasonably good, and it is likely that the cores are failing in 
some cases. It should be remembered that the calculated spin up torque bound- 
aries (dashed lines in Figure 8-4) are only approximate and may be off as 
much as 20%. 

The results of this work showed that the core failure torque was directly pro- 
portional to the core yield strength on bullets of similar shape. I think it is 
obvious that the length of the rifling engraving on the side of the bullet will 
also effect the core failure torque. The core failure torque was also signifi- 
cantly effected by the core temperature. The fact that the core failure torque 
is sensitive to the length of the rifling engraving may explain why some boat 
tail bullets do not perform well in some rifles. In general, a flat base bullet 
will have longer rifling engraving than an equivalent boat tail bullet. 

I finally decided that the only way to prove that core stripping was real, was 
to measure the spin rate of the bullet after it leaves the muzzle, and compare 
the measured value to the spin rate calculated from twist rate and measured 
muzzle velocity. 

Bullet Spin Rate Tests 

If the bullet spin rate is significantly less than the rate determined by the 
muzzle velocity and the barrel twist rate, then either core or jacket stripping 
has occurred. Since there was no evidence of jacket stripping on the recov- 
ered 270 bullets, any reduction in spin rate must be caused by core stripping. 
I first tried using an optical detection device, but after several months of 
unreliable results I decided to use a magnetometer. 

The magnetometer device used to measure spin rate is shown in Figure 8-5, 
and it is nothing more than a square tube measuring 1 " square (inside dimen- 
sion) by 3 feet long. The tube is constructed of 1/4" thick plywood. It has a 1 
inch hole in each end for the bullet to pass through. A rectangular coil 1 .5 X 
1.5 X 31.25 inches is wound on the coil form as shown in Figure 8-6. Holes 
1/8" in diameter are drilled through the form for two 1/8" wooden dowels to 
facilitate winding the coil lengthwise on the form. The coil consists of 35 
turns of #30 ASWG magnet wire. The wire is wound on the form by starting 
at the end of one of the dowels and stringing the wire down one side of the 


Chapter 8: Bullet Core Problems 

Figure 8-5 - Photograph of the magnetometer device used to measure bullet spin 
rate after the bullet leaves the muzzle. 

form to the dowel at the other end. Then the wire goes over the top of the 
form to the other end of the dowel and back down the other side. This proce- 
dure is repeated 35 times to obtain the coil. A 15 ohm resister is connected in 
series with the coil and a 1.5 mfd condenser is connected across the output. 
The condenser reduces the RF noise and the resister provides 0.7 critical 
damping. A shield of aluminum foil is wrapped around the coil to further 
reduce electromagnetic noise. The signal to noise ratio in an extreme RF 
environment is about 200, so a very clean signal is obtained. 

Figure 8-6 - Drawing of the magnetometer showing how the coil is wound on the 
1/4 inch plywood form. The coil form is three feet long and the square hole for 
bullet passage is one inch square. 


Rifle Accuracy Facts 

Figure 8-7 - Photograph of a 270 
bullet with the magnet inserted in 
the 1/16 slot milled into the nose. 
A rare earth magnet is shown 
below the bullet. 

Figure 8-8 - Photograph of an oscilloscope trace 
showing the sine wave signal generated in the 
magnetometer coil by the rotating magnet in the 
nose of the bullet. Horizontal time scale is 0. 1 
msec per cm. Voltage scale is 0. 1 volt per cm. 

The magnetometer is placed with its center about 1 2 feet from the muzzle. 
An Oehler 35P chronograph with 6 foot screen spacing is placed between the 
gun muzzle and the entrance to the magnetometer. A small microphone is 
placed just ahead of the entrance to the magnetometer to trigger the oscillo- 
scope sweep circuit. The bullet has a small (3/16" diameter by 1/16" thick. 
Radio Shack 65-1895) rare earth magnet epoxy bonded into a 1/16" slot cut 
in the bullet nose. When the bullet passes through the coil, the rotating mag- 
netic field produces a sine wave electrical signal (0.5 v peak to peak). A 
photograph of a 270 bullet with the magnet inserted in the nose is shown in 
Figure 8-7 along with a separate magnet. The electrical signal is displayed 
on an oscilloscope and photographed. A typical record is shown in 
Figure 8-8, where you can see that there are about 2.5 complete cycles of 
data. The distortion of the first half cycle is due to the transient response of 
the circuit and is ignored. The period of the oscillation can be measured to 
about 0.2% with this method. The gun is mounted on a machine rest and 
bore sighted, so that the bullet will pass through the one inch diameter en- 
trance and exit holes in the magnetometer. 


Chapter 8: Bullet Core Problems 

The method of testing is to fire a solid copper Barnes X bullet with a magnet 
in its nose with every five test bullets. Because the Barnes X bullet is solid 
copper it has no core to strip. The solid copper bullet serves as a reference 
for the data obtained on the test bullets. The reference bullet tells you what 
the spin rate should be for a given muzzle velocity and is compared directly 
to the spin rate measured on the test bullet. A small correction is made for 
the effect of the small differences in velocity between the reference and test 
bullets. Since the accuracy of the velocity measurements is no worse than 
0.2%, the total error involved in the measurement can’t be more than 0.4% in 
comparing the solid copper bullet with a jacketed lead core test bullet. When 
the core strips the core will have a slower spin rate than the jacket when the 
bullet exits the muzzle. After muzzle exit the core slows down the jacket spin 
rate and the jacket speeds up the core spin rate slightly until both the core and 
the jacket are spinning at the same rate. The bullet then passes through the 
magnetometer and the slower spin rate of the bullet that has stripped its core 
is measured. The measured spin rate difference can be multiplied by about 
1 .5 to estimate the true spin rate difference between the jacket and core when 
the bullet exits the muzzle. This is due to the core being much heavier than 
the jacket. Therefore, its spin moment of inertia is greater than the jackets 
spin moment of inertia. Therefore the slower spinning core will slow the 
jacket more than the faster spinning jacket accelerates the core after the bul- 
let exits the muzzle. I have measured differences in spin rate between the 
reference and test bullets with the magnetometer ranging from 0.0% to 5.5%. 
There can be no doubt that some of these test bullets were stripping their 
cores. The difference in roll angle between the core and the jacket can be as 
much as 20 degrees. In the worst case the spin rate of the jacket, when the 
bullet exits the muzzle, would be about 8.25% higher than the spin rate of the 
core (5.5% * 1.5 = 8.25%). This is a very significant difference. 

The magnetometer spin rate results verified the core failure torque measure- 
ments shown in Figure 8-4 - that is the bullets that were predicted to core 
strip did strip. A summary of the results of some 61 measurements is shown 
below for 10 inch twist barrels. There were five or more records for every 
bullet and the bullet core was considered to have stripped if the difference 
between the predicted and measured spin rate exceeded 1%. 

Rifle Accuracy Facts 



Core Stripping Bench Tests 



270 Winchester - 10" twist 

270 90 gr HP 
270 90 gr HP(hot) 

270 90 gr HP 
270 100 gr HP 
270 100 gr HP 

6mm Remington - 10" twist 

6mm 68 gr match 
6mm 68 gr match 
6mm 65 gr match 
6mm 65 gr match 


































+ indicates pressure higher than shown 

The elevated temperature tests were run by soaking the bullet in a loaded 
round in a pan of boiling water, then firing as quickly as possible. The tem- 
perature of the bullet probably was around 180°F when fired. The 6mm 
pressures were estimated from the 270 data in Chapter 2. This spin rate data, 
combined with the core stripping data tells me that some light hollow point 
bullets have a tendency to strip their cores in a ten inch twist barrel. It is also 
likely that some boat tail bullets suffer from core stripping. There has been a 
lot of discussion in Precision Shooting magazine (1993-1994) about how 
some rifles are inaccurate with boat tail bullets. Unfortunately, the spin test 


Chapter 8: Bullet Core Problems 

is time consuming and expensive at two bucks a pop, so I didn’t do any more. 
I did torque test some medium and heavy weight 270 soft point bullets, and 
with the exception of the one boat tail bullet, none of them appeared to be 
subject to core stripping. Consequently, most commercial bullets of the flat 
base soft point type are probably OK. 

Just how much core stripping contributes to inaccuracy is difficult to say. I 
know that the 6mm 68 grain flat base match bullet performs very well in a 14 
inch twist averaging less than 0.2 inch groups at 100 yards. However, five 
shot groups in a 10 inch twist barrel average over 1 inch at the same muzzle 
velocity. I also know that if you push the 65 grain match bullet too hard in a 
10 inch twist the accuracy deteriorates. Table 10 shows that the 65 grain 
match bullet will core strip if it is pushed too hard. I believe that these results 
tell us that core stripping is significant. 

Many bench rest shooters load their 6mm PPC rifles with very heavy charges 
which results in high chamber pressures (>65,000 psi) and high muzzle ve- 
locities (>3300 fps). If you consult Figure 8-4, you will note that the spin-up 
torques were calculated for a chamber pressure of 50,000 psi. The calculated 
spin-up torque for the 6mm in a 14 inch twist will move upward by 30% for 
a chamber pressure of 65,000 psi. This moves the dashed line for the 14 inch 
twist to where it is just below the dashed line for the 10 inch twist. In other 
words, if you drive these match bullets too hard you may experience core 
stripping even in a 14" twist barrel resulting in the occasional flyer that de- 
fies explanation. 

One other interesting bit of information was obtained as a by-product of the 
bullet spin rate tests. If we compare the measured spin rate with the spin rate 
calculated from the barrel twist rate and the measured velocity, we find that 
the measured spin rate is less than the spin rate obtained from the measured 
velocity by about 2.7%. In one sample case where the measured velocity 
was 3057 fps, the muzzle velocity as determined from the spin rate was 82 
fps less than the measured velocity after correction for chronograph distance 
from the muzzle. This phenomena was described in Chapter 2, and is due to 
the muzzle jet continuing to act on the base of the bullet after the bullet leaves 
the barrel. The muzzle jet accelerates the bullet after it leaves the muzzle but 
the spin rate is not increased because the bullet is no longer in contact 
with the rifling. 


Rifle Accuracy Facts 


Figure 8-9 - Photograph of a sectioned 270 90 grain HP of recent manufacture 
used in testing showing the core projection into the nose that is likely to collapse 
under setback loads. 

Core Collapse 

Unfortunately, the 270 bullet that we chose for this investigation probably 
suffers from core collapse, however I doubt that this is a common flaw in 
bullet design. Figure 8- 9 shows a photograph of the 270 90gr HP bullet of 
the same type that we have been using. You can see that the core projection 
is about 1/8 inches in diameter and extends about 0.15 inches forward in the 
nose of the bullet. Now a quick calculation will show that with a peak cham- 
ber pressure of 50,000 psi the compressive stress acting at the base of the 
core projection, due to the setback acceleration, is approximately 1 2,000 psi 
compared to the yield stress of the lead of 5,000 psi that we measured (see 
Figure 8-2). Obviously, the core projection will fail because the applied stress 
is nearly three times the yield stress of the core. If the core projection stays 
axially symmetrical during collapse, it probably won’t effect accuracy very 
much. However, if it slumps off to the side, it will cause a principal axis and 
CG asymmetry, which do effect accuracy as we will see in Chapter 9. One 
could prove conclusively that the core collapses by using a softer recovery of 
fired bullets than was used in Chapter 7, but that would be a lot of work and 
I don’t think that it is necessary. 

The strange thing about this is that I used thousands of these bullets in the 
1960’s and 1970’s and they performed much better than those of recent manu- 
facture. When I discovered this core collapse problem, I looked around my 


Chapter 8: Bullet Core Problems 


Figure 8-10 - Photograph of a 270 90 grain HP bullet of older manufacture 
showing the shorter core projection that won’t collapse. 

shop and found one of the old 270 bullets and sectioned it. Figure 8-10 shows 
a photograph of this older version of the 270 bullet. You can see that the core 
projection is much shorter than in the newer bullets (Figure 8-9). In fact, it is 
short enough that it could not collapse. So, sometime between the late 70’s 
and mid 80’s the manufacturer changed the design of this bullet and threw us 
a curve right in the middle of this research work. However, the reader should 
realize that this is still an excellent bullet for varmint shooting. 

At this point I decided to switch to a 14" twist barrel to see if I could detect an 
improvement in the 270 accuracy with the 90 grain HP bullet. This would 
lower the spin-up torque acting on the bullet cores and the 270 should shoot 
smaller groups. The test results showed that the average group size decreased 
from 0.804 to 0.505 inches at 100 yards (see Table 1 1, Chapter 9). However, 
a lot of this decrease is due to the reduction in dispersion caused by CG 
asymmetry. Therefore all of the decrease in dispersion can’t be attributed to 
eliminating core striping. 

The 6mm 65 gr HP is satisfactory for the 6mm with a 10 inch twist as long as 
we don’t overload it. Unfortunately, these bullets are no longer available 
after the untimely demise in 1994 of Walter Jankowski, owner of Cook Bul- 
lets. So I switched to a 14 inch twist barrel on the 6mm BR bench rest gun 
and started using the 68 grain match bullets from a different manufacturer. 
The results of these changes are shown in Chapter 9 which deals with the 
effects of bullet imbalance. 


Rifle Accuracy Facts 

Effect Of Spin-Up Torque On Accuracy 

Every now and then I read an article in a gun magazine about how the rifle 
rotates as a result of the bullet spin up torque, and how this rotation causes 
inaccuracy. There are never any facts or data in these articles, just an opin- 
ion. Well it is easy to take the spin up torque that we calculated in the early 
part of this chapter and estimate the amount of angular rotation of the gun. 
The spin up torque calculated for a 90 grain 270 bullet was 15 inch-pounds. 
We can scale this up for a 130 grain bullet, and the torque will be 22 inch- 
pounds. We can estimate the spin moment of inertia of the rifle, and from the 
moment of inertia and torque we will get an average angular acceleration of 
203 rad/sec 2 . If we multiply the angular acceleration by the time that the 
bullet is in the bore (1.3 msec), we get an angular rate of 0.26 rad/sec. We 
can also calculate the angle that the rifle rotates, and that turns out to be 
0.01 degrees. If the CG of the rifle is one inch below the bore centerline, 
the barrel will be deflected to the left at a rate of 0.26 inches/sec and will 
translate about 0.013 inches at 100 yards. If the spin torque varies 1% from 
shot to shot, which is typical of the velocity variation, then the variation in 
lateral velocity is 0.0026 rad/sec, which will cause a horizontal dispersion of 
0.00025 inches at 100 yards. The variation in lateral translation of the barrel 
is 0.00013 inches. This is a rough engineering estimate of the torque effect, 
however it can’t be off enough to change the conclusion that the torque effect 
is too small to worry about on a rifle. However, it could be significant on 
pistols. I didn’t check it, so I don’t know, but there are so many other prob- 
lems in pistols, it may not be important. 


The fact that the lead cores in bullets sometimes strip due to the large spin up 
torques acting on the bullet jacket was demonstrated by measuring the spin 
rate after muzzle exit using a magnetometer approach. The torque required 
to cause core stripping was measured with a torque wrench on four test bul- 
lets at room temperature (70°F) and at elevated temperatures (250°F). The 
torque required to strip the cores at room temperature was considerably larger 
than the torque required at the higher temperatures. Also, harder core mate- 
rial reduces core stripping because it is stronger. These bench tests were in 
qualitative agreement with the measured spin rate and group size tests. 




B ullet imbalance is one of the largest contributors to dispersion, and I 
have known about it for nearly 30 years. However, the problem was that 
it has only been in the last several years that I have really understood exactly 
how it causes dispersion. Also, aside from making or buying perfect bullets, 
I couldn’t find a way to correct the situation. So, let’s start out by under- 
standing the problem. 

Physical Explanation 

Figure 9-1 demonstrates how bullet imbalance causes the bullet to be de- 
flected when it leaves the muzzle. The sketch on the left side of Figure 9-1 
shows how the center of gravity (CG), which is offset from the center line or 
geometric axis, is forced to rotate about the geometric axis. This is an un- 
natural condition. A spinning projectile will always spin about its principal 
axis and the principal axis always passes through the projectile CG, if it is 
free to do so. Consequently, the bullet will start spinning about its principal 
axis and its CG the instant it exits the muzzle. However, due to the CG offset 
a tangential velocity component (Vt) was produced while the bullet was in 
the bore. This tangential velocity component (Vt) will be maintained as a 
lateral drift velocity (Vd) when the bullet exits the bore. The direction of the 
lateral drift velocity will be perpendicular to the plane containing both the 


Rifle Accuracy Facts 

Figure 9-1 - Sketch showing how bullet imbalance causes a lateral drift velocity, 
which causes deflection of the bullet trajectory as it leaves the muzzle. 

geometric and principal axes at the instant of muzzle exit. The distance that 
the bullet will deflect can be obtained by multiplying the lateral drift velocity 
by the time of flight. The equation that calculates the amount of bullet deflec- 
tion at the target is 

a = 24 n (V/t) (TOF) 8 

a = bullet deflection in inches, radius of dispersion or miss distance. 

n = pi = 3.14159 

V = velocity at the muzzle in fps. Note that V is about 50 to 1 00 fps less 
than the instrumental velocity (2900 fps). This results from the 
muzzle blast continuing to accelerate the bullet after it leaves the bore. 

t = twist rate in inches per revolution (10 inches). 

TOF = Time of Flight (0.1 second at 100 yards). 

8 = CG offset in inches. 


Chapter 9: Bullet Imbalance 

Figure 9-2 - Photograph ot a 270 
bullet modified by drilling a hole to 
deliberately produce an exaggerated 
CG offset of 0.00118 inches. 

In the next section we will experimentally determine the radius of dispersion 
for a CG offset of 0.001 1 8 inches. This is three to four times the maximum 
CG offset to be expected in a production bullet. This value of CG offset was 
determined by the diameter and length of the hole drilled in the side of the 
bullet used in the experiment that follows. Let’s calculate the radius of dis- 
persion to be expected at 100 yards from this oversize CG offset. 

a = 24*3. 1 4 1 59*(2900/ 1 0)*0. 1 *0.00 1 1 8 = 2.58 inches 

In 1909 Dr. Franklin Mann published a book (Reference 21) with an equa- 
tion that is equivalent to the one presented here. While his equation was 
correct and he tested it experimentally his physical reasoning was flawed. 
However, this was a remarkable book for its time. Now we will experimen- 
tally evaluate the effect of CG offset. 

Experimental Evaluation 

We again turn to the “Olde Engineers Trick” of exaggerating an effect so that 
it can be easily measured. This time we deliberately unbalance the 90 grain 
270 bullets by drilling a hole in the side of the bullet that goes exactly half 
way through. The hole is placed at the longitudinal CG position. Figure 9-2 
shows a picture of a bullet that has been modified to obtain a CG offset of 
0.001 18 inches. Figure 9-3 is a plot showing the bullet holes from four 
3-shot groups fired with the hole up, right, down, and left at muzzle exit. The 
square symbols show the center of each group, and the circular sketches near 
the group show the direction of the hole in the sides of the bullets when they 
exit the muzzle. If you look at group 1, you can see that the hole in the bullet 
points up at muzzle exit, which means that the CG of the bullet was below the 
geometric axis. With a clockwise direction of rotation (right hand twist), the 
CG in group 1 is translating to the left, which means that the bullet will be 
deflected to the left, as it was. If you draw a circle with a radius of 2.5 inches, 
you can see that it passes close to the centers of all four groups. In the 


Rifle Accuracy Facts 


J M 2 C2 u 

■ = Gl 













— 2.5 

















O = B 






-4 -3 -2 -1 0 12 3 4 


Figure 9-3 - Plot of a target showing four 3-shot groups formed by indexing the 
bullets in 90 degree increments in roll angle. The bullets had a large CG offset of 
0.00118 inches. The experimentally determined radius of dispersion at 100 yards 
was approximately 2.5 inches. 

previous section we calculated a value of 2.58 inches for the radius of disper- 
sion. Roll angle is simply the angle of rotation about the geometric axis 
(centerline) of the bullet. If you try this test, be sure to remove the extractor 
and the ejector and have ample headspace between the bolt face and car- 
tridge head. Otherwise you will rotate the cartridge in a random fashion and 
the results will be a mess. Under ordinary conditions the direction of deflec- 
tion is completely random, depending on the roll angle orientation of the CG 
asymmetry. This test confirms our diagnosis of the problem and determines 
the sensitivity of dispersion to the amount of CG offset. The question now is, 
how badly balanced are production bullets? Unfortunately, that requires a lot 
more work, but it can be done. 

Measured Bullet Imbalance 

There are two ways to measure bullet imbalance — static and dynamic. Static 
balance is the easiest but least accurate and slowest method. 


Chapter 9: Bullet Imbalance 

Figure 9-4 - Photograph of a device that checks the static balance of bullets. The 
design is based on the principle of the torsional pendulum. See Appendix C for 
complete description. 

Figure 9-4 shows a static balance rig. It is based on the idea of a torsional 
pendulum where the cradle that holds the bullet is suspended between two 
lengths of tightly stretched steel wire. As the bullet is rotated, the cradle will 
rotate if there is a CG offset, and deflect a light beam which produces a light 
spot on a screen. The motion of this light spot is an indication of the amount 
of bullet CG offset. The device is balanced by the nut on the screw on the top 
of the cradle, and the vane hanging down between the two magnets damps 
the rotational motion. Construction, calibration, and use of this device is 
described in detail in Appendix C. The results of measuring the CG offset on 
a box of one hundred 90 grain 270 HP bullets are shown in a bar graph in 
Figure 9-5. It can be seen that most of the bullets have a CG offset between 
0. 1 and 0.2 mils, while some of them are unbalanced by about 0.3 mil. This 
is typical of ordinary commercial bullets. Custom match bullets have about 
one third this amount of CG offset. Bear in mind that the 90 grain 270 HP is 
intended for varmint shooting and is certainly accurate enough for that use. 

A dynamic balance device is shown in Figure 9-6. In this device, the bullet is 
spun at 120 revolutions per second (rps) in an air bearing suspended between 


Rifle Accuracy Facts 

Figure 9-5 - Bar chart showing the results obtained in checking the static balance 
of a box of 100 caliber 270 bullets. 

Figure 9-6 - Photograph of a dynamic 
balance device used to check the 
balance of bullets. It is based on the 
principle of the air bearing, where the 
unbalanced bullet spins inside the 
plastic cylinder producing an oscillating 
force on the two earphone diaphragms. 
This motion produces an oscillating 
electrical signal proportional to the 
imbalance. See Appendix C for 
complete description. 

two magnetic microphones that serve as electrical transducers. As the bullet 
spins, without touching the inside surfaces of the plastic cylinder, the air 
pressure between the spinning bullet and the walls of the cylindrical cavity 
force the cylindrical carrier to oscillate. This mechanical oscillation is trans- 
mitted to the diaphragms of the two headphones and converted to an electri- 
cal signal, which can be observed on an oscilloscope. Construction, calibra- 
tion, and operation of the dynamic balance device is also described in detail 
in Appendix C. The results of checking the balance of the same box of one 
hundred bullets checked by the static balance method is shown in Figure 9-7, 
and it can be seen that the results are essentially the same. However, the 


Figure 9-7 - Bar chart showing results of measuring the dynamic imbalance of the 
same 100 bullets used in the static balance measurement shown in Figure 9-5. 

Miss distance at 100 yards for a given imbalance is shown on the top scale. 

dynamic balance data are smoother and probably more accurate than the data 
obtained from the static balance device. The dynamic device is much easier 
to use and is more accurate, but it is much more difficult to make than the 
static balance device. 

At the top of the graph in Figure 9-7 the miss distance (radius of dispersion) 
in inches is shown for the corresponding CG offset. I developed a computer 
program that uses a random number generator to pick both the CG offset and 
roll angle orientation, and “fire” twenty 5-shot groups. I found that the aver- 
age group size using this computer program with the same 100 bullets in 
Figure 9-7 would be around 0.7 inches with a 10 inch twist barrel. The maxi- 
mum computed group size was 1.3 inches and the minimum group size was 
0.3 inches. This compares favorably with the last accuracy test fired in Chapter 
8, so there is little doubt that bullet imbalance accounts for most of the re- 
maining inaccuracy in the experimental rifle. 

I hasten to point out that the measured imbalance on this particular bullet is 
typical of ordinary production bullets that I have tested. In fact, I have found 
bullets of other manufacture that were worse. The most likely cause of bullet 
imbalance is the circumferential variation in jacket wall thickness, that 


Rifle Accuracy Facts 

results from deep drawing a flat copper disk to form the jacket. In fact, I am 
amazed that bullets can be made as accurately as they are in mass production. 
When you measure bullet jacket thickness run out at the same distance from 
the base of the bullet, you find circumferential variations consistent with the 
CG offsets that we measured. The manufacturer states in their brochure that 
their hunting bullet jackets are held to a maximum of 0.6 mil and their match 
bullets to 0.3 mil jacket concentricity. Since the jacket of these 90 grain 
hollow points is about 1/3 of the total weight, the CG offset is about 2/3 of 
the jacket concentricity. This means that the CG offset will be about 0.4 mil 
for ordinary bullets and about 0.2 mils for their match bullets. The 0.4 mil 
imbalance agrees well with the measured data in Figure 9-7. The CG offset 
is, of course, caused by the fact that lead is much heavier than copper. Some 
match bullets are held to less than 0. 1 mil CG offset. I tested 6mm 68 grain 
match bullets and got a maximum CG offset of about 0.07 mils. You would 
never be able to average 0.2 inch five shot groups at 100 yards with a bench 
rest rifle if the bullets weren’t balanced to 0. 1 mil or better. Match bullets are 
shorter than hunting bullets and are made with thinner jackets, which I guess 
would make the jackets easier to draw with uniform thickness. Unfortu- 
nately, the jacket thickness of general purpose bullets has to be kept where it 
is for reliable expansion characteristics on game animals. Consequently, I 
doubt that any manufacturer will be able to produce ordinary bullets that are 
significantly better than they are now, unless somebody comes up with a 
better way of making bullet jackets. What we need is some way of compen- 
sating for bullet imbalance before the bullet leaves the barrel. 

Bullet Balance Compensator 

The trick to solving the bullet imbalance problem would be to allow the bul- 
let to spin about its centroidal axis before leaving the barrel. The centroidal 
axis passes through the CG and is parallel to the geometric axis. If this could 
be done, the barrel would decrease the lateral drift velocity and decrease the 
effect of bullet imbalance. I tried three approaches to making a compensator 
and all three attempts failed. 

The first approach was to counterbore the muzzle for a distance of three inches. 
For this to work the radial clearance between the bullet and bore must be 
small (less than 3mils). The reason for this small clearance is that the 


Chapter 9: Bullet Imbalance 

corrective effect depends on viscous interaction between the bullet and the 
barrel. I tried this starting with a 1 mil radial clearance and the groups were 
enormous. I gradually increased the clearance and at about a 10 mil radial 
clearance the gun shot about as well as it did before modification. After 
doing the muzzle blast shadowgraph tests and seeing the small partially burned 
powder granules traveling along with the bullet, I have doubts about this 
method ever working. Also, after testing I sectioned the barrel and found that 
the counterbore was off center. So that may have doomed the test from the 
start. If anyone wants to try this, I suggest making piloted reamers in 1 mil 
increments. According to computer calculations it should work, but I may 
have missed something in the physical model. 

Another way to compensate for CG offset would be to allow the barrel to 
move about the bullet CG before the bullet exits the muzzle. I tried two 
different approaches and neither one worked. One of them appeared to be 
trying to work but it drew straight lines of bullet holes as a result of thermal 
distortion. I tested the barrel on the bench and found that the muzzle warped 
enough with a modest change in temperature to explain the drift. 

While I haven’t given up on this problem I decided to go ahead and publish 
this book because it is a difficult problem that may not be solvable. Mean- 
while all you can do is buy the best bullets that you can find. It also should be 
pointed out that bullet manufacturers are continually trying to improve the 
quality of their bullets and since this data was taken some time ago the situ- 
ation may have changed by now. 

Bullet Making 

I would rather have a root canal operation on a tooth than make my own 
bullets, but I have been forced to make some special bullets on occasion. 
There have been a number of articles on custom bullet making and I take 
issue with some of their recommendations. One of these procedures is lubri- 
cating the slugs before they are swaged into cores. Lead wire is cut into slugs 
that are slightly heavier than the swaged cores. The slugs are then lubricated 
with a mixture of vaseline and lanolin, although other lubricants have been 
used. This is usually accomplished by rolling the slugs on a cotton cloth that 
has been coated with lubricant. Another way is to mix a known amount of 
lubricant into a known volume of solvent and then dip the slugs into the 


Rifle Accuracy Facts 

solution. The solution is drained off and the solvent allowed to evaporate 
leaving a thin uniform coating of lubricant on the slugs. This would seem to 
be the preferred method because the coating should be thin and uniform. The 
lubricated slugs are then swaged into cores in the core swaging die where the 
excess lead is bled off. The cores are then degreased with a solvent. Methyl- 
ene chloride is commonly used since the EPA has restricted the use of trichlo- 
rethylene and 1,1,1-trichloroethane. The problem is that the solvent is usu- 
ally used over and over, which results in the concentration of lubricant in the 
solvent increasing with repeated use. This can result in a thin coating of 
lubricant being left on the cores. To avoid this problem some bullet makers 
degrease the cores by passing them through a series of three or four contain- 
ers of solvent that are frequently replaced so that the last container remains 
relatively free of solubilized lubricant. This technique requires a lot of sol- 
vent but is preferred over repeatedly using the same batch of solvent. The 
use of lubricant can cause potential problems. If lubricant is left on the cores, 
then core stripping may occur during bullet spin-up causing dispersion. Also, 
lubricant could be trapped in the surface of the lead when the slugs are swaged 
into cores. This would cause a center of gravity offset in the finished bullet. 
I have never found it necessary to lubricate the slugs prior to swaging them 
into cores. In fact, I first clean and degrease the slugs by tumbling them in a 
water solution of detergent (Lemon Joy) before swaging them into cores. I 
also clean the swaged cores in the same manner just to make sure that they 
are clean. However, I haven’t made the volume of custom bullets that some 
bench rest shooters make so there may be a need for lubricant in these large 
volume situations that I’m not aware of. 

In this business “Cleanliness is next to Godliness.” In fact, match bullets 
should be made in same type of clean room that is used in the production of 
electronic chips. All it takes is a very small speck of foreign matter either in 
or on the lead core or the inside of the jacket to cause the one flyer in one 
group that causes you to lose a match. 

The problem of jacket concentricity is one of the limiting factors at the mo- 
ment and I have tried to correct jackets with machining with no success. 
Maybe you could use a boring tool in a super accurate lathe with essentially 
zero (<100 pinches) spindle runout and improve the jackets, but I doubt it. 
Lathes this good do exist in large shops but they are expensive and difficult to 
keep in adjustment. The best match jackets come from a company called J-4 
which apparently is connected with Berger Bullets and they are very good. 


Chapter 9: Bullet Imbalance 

I think I have already mentioned the fact that I accidentally found a small 
void in the lead core of a sectioned bullet that would have caused a large CG 
offset. It was probably caused by a small piece of slag that was in the lead 
wire. Short of X-raying every core, I don’t know how one makes sure the 
cores are uniform. Of course, this would be prohibitively expensive in 

Another problem with hollow points is that the top surface of the core may 
not stay flat and perpendicular during the point swaging operation. The core 
may also bleed by the edge of the punch in the core swaging operation, caus- 
ing a flash at the core jacket junction. These problems can cause a CG offset 
and principal axis misalignment. I have observed this problem on commer- 
cial bullets that I sectioned and as you would expect they shot very poorly. 
Leaving a short (0.06") core projection like we see in Figure 8-10 helps to 
alleviate this problem by reducing the amount of diameter reduction at the 
front of the core. Just don’t make it too long. This problem makes you 
wonder what happens to the core when it is swaged into the rifling in the 
throat during spin up. Does the core stay symmetrical? Nobody knows. You 
might be able to test this by testing the dynamic balance before and after 
firing using a very soft recovery. I don’t plan on doing it because it would 
take an enormous amount of effort. It may be that slender nose bullets per- 
form well because there is less length of bullet in contact with the rifling. 
Some bench rest shooters seem to get superior performance from these bul- 
lets with slender noses but I have not had that experience. 

There is another problem with hollow point cores that extend too far forward 
into the ogive nose. When the ogive nose is formed the jacket collapses in 
short segments and is usually not uniform in thickness. If the core is swaged 
into this forward portion of the jacket it could produce a CG asymmetry. 

Some of the commercial bullet makers are turning out match grade bullets 
that are pretty good as far as balance is concerned. Commercial bullets have 
improved a lot in the last 30 years. However, the custom hand made bullets 
still win practically all of the bench rest matches. I would guess that the 
difference is in quality of the jackets plus you can discard a bullet that 
didn’t “feel right” during swaging. An ordinary machine doesn’t have that 


Rifle Accuracy Facts 

If you decide to make your own bullets be sure to use a slightly rounded heel 
at the base of the bullet. A sharp corner combined with the rifling lands can 
produce small fins, which can break off as a result of the muzzle blast. I have 
seen this in old spark shadowgraphs and recovered bullets and it will cause 
an asymmetry. As far as I am concerned, making your own bullets is a losing 
proposition unless you need to try a new idea or you want to do it for the 
“fun” of it. It would help to be slightly crazy! 

Accuracy Test 

This is the final accuracy test on the 270 experimental rifle with a 14" twist 
barrel. You may recall that in the last test in Chapter 7 (Table 8) we had an 
average group size of 0.804 inches at 100 yards using 90 grain hollow point 
bullets with a 10" twist barrel. We also estimated with the theory in this 
chapter that the 270 should average about 0.7 inches at 100 yards, if bullet 
imbalance was the only error contributing to dispersion. Consequently, we 
should expect 0.7*10/14 = 0.5 inches average group size with the 14" instead 
of a 10" twist barrel, with no other rifle errors contributing to dispersion. 
The results of the test of the 270 with a 14"twist barrel are shown in Table 11. 

270 Winchester Accuracy Test 
with 14 inch twist barrel and 90 grain HP bullets 

Extreme Spread For Twelve 5-Shot Groups At 100 Yards 

Average Maximum Minimum 

0.505 0.617 0.393 

I think this test shows that most of the dispersion left in this experimental 
rifle is due to bullet imbalance. I also believe that this gun would average 
around 0.2 inch groups at 100 yards with match grade bullets and a 14" twist 
barrel. Unfortunately 270 match bullets are unavailable at this time. This 
concludes our work on the 270 sporter. 



E xternal ballistics or flight dynamics is the study of the motion of the 
bullet after it leaves the muzzle. We have already used the Six Degree 
Of Freedom (6DOF) trajectory computer program (code) to examine the ef- 
fect of bullet center of gravity (CG) offset and the effect of muzzle blast on 
the trajectory of a canted bullet. We will find out how a bullet actually moves 
in flight and how this effects accuracy. All of the work done in this chapter 
will be for a right hand twist barrel. Right hand twists are the normal way of 
rifling barrels but occasionally a few people use left hand twists. In the case 
of a left hand twist the direction of the coning motion is reversed. We start 
out with a brief description of the 6DOF computer code. 

6DOF Trajectory Code 

The 6DOF computer code is an invaluable tool for investigating the detailed 
motion of a projectile. It does this by solving the three translational equa- 
tions of motion and the three angular equations of motion. These equations 
are shown in Appendix D. The three angular equations predict the angular 
motion about the roll (spin), pitch and yaw axes. The output from the angular 
motion equations are used in the translational equations to predict where the 
projectile is going in space. The six equations of motion are solved simulta- 
neously by the computer. In order to use the 6DOF code one must know the 


Rifle Accuracy Facts 

initial conditions, several aerodynamic coefficients, and the mass character- 
istics of the projectile. Unfortunately, these codes are not user friendly and 
are usually used only by professionals. The biggest problem is finding the 
aerodynamic coefficients for a particular bullet shape. This requires an ex- 
tensive library which most people don’t have. At any rate, we will be using 
this code extensively and it is very precise if you know the aerodynamic and 
mass characteristics. 

Gyroscopic Stability 

A lot has been written about gyroscopic stability, but most of this material 
really doesn’t show the reader how it effects the motion of the bullet and 
accuracy. With the 6DOF computer program we can show the angular con- 
ing motion of the bullet in detail. Figures 10-1 through 10-4 show the coning 
motion of a bullet for four gyroscopic stability factors (GS) ranging from 
1.13 to 2.98. These figures show the angle of attack in the vertical plane 
(pitch) on the vertical axis versus the angle of sideslip (yaw) on the horizon- 
tal axis where the bullet is launched with an initial angle of attack of about 
0.2 degrees in Figures 10-1 to 10-3. A smaller angle of 0.13 degrees was 
chosen for Figure 10-4. The initial angle of attack of 0.2 degrees was chosen 
because it is probably typical of the maximum initial angle of attack that 
would be present in a good rifle with a chamber and throat on the center of 
the bore. The initial angle of attack is probably considerably less on a good 
bench rest rifle using cases with turned necks and bullets seated in contact 
with the lands. The best way to interpret these figures is to imagine that you 
are viewing the bullet from the rear along the flight path and watching the 
motion of the nose of the bullet. Of course the bullet is flying along a cork 
screw trajectory around the average flight path. The effect of the cork screw 
motion on dispersion is considered later. Notice that the bullet starts out with 
a high frequency (fast precession) coning motion that damps out fairly quickly 
and the motion settles down to a lower frequency coning motion (slow pre- 
cession). The higher the gyroscopic stability the lower the slow precession 
frequency and the higher the fast precession frequency. However, the higher 
the gyroscopic stability the faster the slow precession damps. This is desir- 
able because the slow precession coning motion is the most persistent. Note 
that in the case where GS=1 .13 (Figure 10-4) the slow precession grew rap- 
idly from an initial angle of attack of 0.13 degrees to a maximum angle of 


Chapter 10 : External Ballistics 

Figure 10-1 (Left) - Plot of 6DOF computer flight simulation showing the coning 
motion of a bullet with a large gyroscopic stability factor (GS) of 2.98. If one were 
looking along the flight path of the bullet, the motion of the nose of the bullet would 
appear as the spiral motion seen on the graph. The bullet is launched at the muzzle 
with an angle of attack of 0.2 degrees and impacts at 200 yards. Notice that there is 
a high frequency component (fast precession) that quickly damps and a slow 
component of motion (slow precession) that persists. 

Figure 10-2 (Right) - Plot showing the angular motion of a bullet with a GS of 
1.91 launched with a 0.2 degree initial angle of attack. Notice that the precession 
frequencies are slower than those on the previous graph where the GS 
was 2.98 and that the coning motion takes longer to damp. 


Rifle Accuracy Facts 

Figure 10-3 (Left)- Plot showing the coning motion of a bullet with a GS of 1.41 launched 
at an angle of attack of 0.2 degrees. This GS is typical of a 6mm 68 grain match bullet. 

Figure 10-4 (Right)- Plot showing the coning motion for a bullet launched at 0. 13 
degrees angle of attack with a very low GS of 1. 13. You can see that the coning 
motion hardly damps at all over a 200 yard range compared to the previous three 
figures. Also note that the angle of attack grows rapidly from the initial angle to an 
angle of 0.25 degrees. This motion is typical of any bullet with a low GS and a 
normal ogive shape. 


Chapter 10: External Ballistics 

attack of 0.25 degrees and has damped down only slightly at a range of 200 
yards. These 6DOF computer simulations were run for a 90 grain 270 bullet 
for twists of 8, 10, 1 1.6 and 13 inches at an altitude of 5000 feet above sea 
level just as a demonstration. However, the coning motion is valid for any 
caliber bullet with an ogive nose and flat base with the same gyroscopic sta- 
bility factor. At sea level the GS values would be about 16% lower. The 
typical gyroscopic stability factor for a 6mm 68 grain hollow point bullet is 
about 1 .4 in a 14 inch twist at sea level (Figure 10-3) and would be about 1.6 
at 5,000 feet altitude. We will determine the gyroscopic stability factor for a 
6mm 68 grain bullet experimentally later in this chapter under wind drift. 

Figure 10-5 shows how the maximum coning angle varies with gyroscopic 
stability. Note that even though the initial angle of attack remains constant at 
0.2 degrees the maximum coning angle increases to about 1 degree as gyro- 
scopic stability approaches 1 .0. The radius of the corkscrew motion caused 
by the coning motion also increases rapidly as the GS decreases to 1 causing 
significant dispersion. You can get away with a low GS (slow twist) at high 
altitudes and warm temperatures, but a combination of low altitude, high 
atmospheric pressure and low temperature can shift the data points to the left 

Figure 10-5 - Plot showing how the maximum coning angle varies with gyroscopic 
stability factor (GS). As GS decreases to one the maximum coning angle and the 
radius of the corkscrew motion increases very rapidly. Abnormal atmospheric 
conditions (high pressure, low temperature) will reduce GS by 20% or more. 
This can cause a normally stable bullet to become violently unstable. 

1 85 

Rifle Accuracy Facts 

- 0 . 003 - 0.002 - 0.001 0 0.001 0.002 0.003 0.004 


Figure 10-6 - Plot showing the coning motion at a GS of 2.98 where the bullet is 
launched at a zero angle of attack but gravity drop causes a very small induced 
angle of attack. Purpose of the plot is to show how the bullet gradually points 
its nose to the right for a right hand twist as a result of gyroscopic effects known 
as yaw of repose. Note that the scale is 100 times more sensitive than it was on 
Figures 10-1 through 10-4 and that the angles are very small. 

more than 20%. This would cause a 6mm bullet in a 15 inch twist (GS=1.2) 
to become gyroscopically unstable, which would result in large dispersion. 

Just to show you another feature of the bullet’s coning motion a simulation 
was run that is identical to that shown in Figure 10-1, except that the bullet 
was launched with no disturbance (Figure 10-6) to show the effect of yaw of 
repose. The coning motion results from the action of gravity on the bullet 
causing a small angle of attack as soon as it leaves the muzzle. Note that the 
scale is 100 times more sensitive than it was in Figures 10-1 through 10-4 
and that the angles are very small. You can see in Figure 10-6 that the bullet 
has a low amplitude coning motion that damps down with the bullet pointed 
to the right for a right hand twist barrel. This is called yaw of repose and the 
drift to the right is caused by gyroscopic effects resulting from the downward 
curvature of the flight path. The yaw of repose angle causes the bullet to drift 
to the right 0.215 inches in 200 yards. This yaw of repose effect does not 
cause an accuracy problem because it is consistent from shot to shot. How- 
ever, it does have an effect on the vertical component of wind drift which we 
discuss later in this chapter. 


Chapter 10 : External Ballistics 

It is possible to calculate both the slow and fast precession frequencies and 
the motion from an analytical theory (Tricyclic Theory) developed to a high 
degree of sophistication in the 1950’s and 1960’s by the author and others 
(References 22 and 23). This is a very useful tool used by the pros to analyze 
flight dynamics problems. We are going to look at two simple equations that 
allow one to calculate the two precession frequencies. If the reader is math- 
ematically inclined the equations tell you how the frequencies are effected 
by various changes. The fast precession (FI) and the slow precession (F2) 
frequencies are 

FI = [(p*Ix)/(2*I) + { [(p*Ix)/(2*I)] 2 - [Ma/I] }] l/2 /( 2*n), cps 
F2 = [(p*Ix)/(2*I) - { [(p*Ix)/(2*I)] 2 - [Ma/I]}] 1/2 /(2*7t), cps 


p = spin frequency (spin rate) in radians per second, radians per second 

= cycles per second * 2n 

lx = spin moment of inertia, slug-ft 2 = pound-ft 2 /g 
I = lateral moment of inertia, slug-ft 2 

Ma = slope of the aerodynamic pitching moment with respect to 
angle of attack (a) 

The moments of inertia can be calculated but they can be more accurately 
determined by experiment. Now the fast precession frequency (FI) is usu- 
ally roughly one tenth of the spin frequency (spin rate) and the slow preces- 
sion frequency (F2) is about one sixth the fast precession frequency for an 
average length bullet. For instance in Figure 10-2 where the spin frequency 
is 3600 cycles per second (cps), FI should be about 360 cps and F2 about 60 
cps. Well the actual frequencies in Figure 10-2 for FI and F2 are about 450 
and 75 cps. The reason for this discrepancy is that the Ix/I ratio is larger for 
a short 90 grain bullet than the normal length 130 grain 270 bullet. In the 
case of a 90 grain bullet the ratio of FI to spin frequency should be more like 
one eighth. A 6mm 68 grain bullet would have similar ratios. 

Notice that Ma is always a positive number for a bullet that is aerodynami- 
cally unstable but is gyroscopically stable. Note that all normal bullet shapes 
are aerodynamically unstable and would tumble without being spun at a high 


Rifle Accuracy Facts 



M = 


Figure 10-7 - Sketch showing how the lift force acting forward of the center of 
gravity results in a nose up unstable moment about the CG. 

rate. Figure 10-7 shows a sketch of how the aerodynamic pitching moment is 
developed. When the bullet has an angle of attack (or sideslip or both) with 
respect to the free stream air flow (or trajectory) a lift force is developed 
which has a center of pressure ahead of the CG in a normal situation. This 
causes the bullet to rotate nose up thereby increasing the angle of attack. 
Consequently, it is an unstable moment. If the gyroscopic stability is large 
enough it prevents the angle of attack from increasing. The moment on an 
aerodynamically stable body, such as a rocket with tail fins, has a negative 
Mot or stable pitching moment, because the total lift force acts on the body 
behind the CG. Now look at the equations for FI and F2. If Ma /I is larger 
than [(p*Ix)/(2*I)] 2 then the square root of a negative number results, which 
is a “no-no” in mathematics and means that the projectile is gyroscopically 
unstable. This leads us to define the gyroscopic stability factor (GS) as 

GS = [(p*Ix)/(2*I)] 2 /[Moc/I], GS > 1 

where GS must be equal to or greater than 1 for gyroscopic stability. Now, 
not to worry about trying to calculate this thing, because I will show you a 
simple way to measure the gyroscopic stability in the section on wind drift. 


Chapter 10 : External Ballistics 

The reasons for going through all this is first to show you the correct way of 
calculating gyroscopic stability and how it was derived, but second and more 
important the equations show you how the gyroscopic stability is affected by 
the spin rate, moments of inertia and aerodynamics. 

For instance, we can show that GS is independent of velocity except for the 
small effect of Mach number on Ma, because both the square of the spin rate 
p and Ma are proportional to the square of the velocity. Mach number is 
simply the velocity V divided by the speed of sound a. 

M = V/a 

where the speed of sound is 

a= 1117*[(°F+460)/519] 1/2 , feet/sec = 1130 fps @ 70°F 

Figure 1 0-8 shows the effect of Mach number on Ma in aerodynamic coeffi- 
cient form for the 7.62 mm NATO bullet (Reference 24). You can see that as 
the bullet slows down on a long range trajectory the Mach number decreases 
and the moment coefficient (Ma) increases. This means GS decreases at 
long range and in some cases the effect may be great enough to cause a bullet 

Figure 10-8 - Graph showing how experimental pitching moment coefficient 
increases with decreasing velocity and Mach number. This is a destabilizing effect. 


Rifle Accuracy Facts 

Figure 10-9 - Effect of varying angle of attack on pitching moment slope Ma at 
3000 fps. Bullet is more stable at higher angle of attack. 

to become unstable. This particular bullet has a GS of 1 .3 at 2034 fps (M = 
1.8) and a GS of 2.2 at 3164 fps (M = 2.8). This velocity excursion corre- 
sponds to a range of roughly 600 yards when the bullet is launched at a muzzle 
velocity of 3164 fps. 

So far we have treated Ma as being a constant with respect to angle of attack 
(a), but this is only true for small angles. Figure 1 0-9 shows a typical varia- 
tion of the pitching moment (M) as a function of angle of attack (a). You can 
see that the slope of the curve (Ma) decreases as the angle of attack increases. 
This means that the bullet becomes more stable as the angle of attack in- 
creases. This means that a bullet with a GS approaching 1 at long range may 
be stable at a small coning angle (angle of attack). In this case the nose will 
travel in a circle at whatever angle it is stable. This is known as a limit cycle 
and in fact, that is what happens with the 7.62 mm round at long range. So 
you see, life can get complicated in this business. 

Air density has a considerable effect on Ma since it is proportional to den- 
sity. The higher the density the smaller the GS. The following table shows 
the effect of altitude on density at an air temperature of 70°F. 


Chapter 10: External Ballistics 



The Affect Of Altitude On Air Density 





Density Ratio 

Density Factor, o 
(1/density ratio) 

Sea Level 












































Note: #/cf = pounds per cubic foot 
Density Ratio = density/(density at sea level) 

The density factor is the reciprocal of the density ratio and should be multi- 
plied times the GS. Of course, the GS at 10,000 feet will be 1.35 times that at 
sea level or 35% greater. What this means is that if you live at sea level your 
bullets will be more gyroscopically stable at high altitude. 

Air temperature also effects the air density. Density is inversely proportional 
to the ratio of absolute temperature. The absolute temperature (°Rankine) is 
equal to the temperature in °F added to 459°. For instance the density at 
100°F (549°R) is 12% less than it is at 30°F (489°R). This means that the 
gyroscopic stability will be 12% less at the colder temperature. Atmospheric 
pressure and humidity also effects air density. Atmospheric pressure can 
typically vary by 7% between a High and a Low pressure area and have a 
proportional effect on density at the same temperature. Atmospheric humid- 
ity can cause a density change of 2.4% between 0% and 100% humidity. A 
high humidity decreases density - which is just opposite to what most people 
would guess. The humidity is usually lowest at low temperatures. So, if you 
shoot in a high pressure region at a low temperature you could have a 


Rifle Accuracy Facts 

gyroscopic stability factor (GS) reduction of 20% or more compared to ideal 
conditions (low atmospheric pressure and high temperature). If you are us- 
ing a slow twist barrel (15 inch) where the GS is as low as 1.2 under ideal 
conditions, you will have an effective GS of less than 1 and the bullets 
will be unstable. 

We should also note that the GS is inversely proportional to the square of the 
twist rate and inversely proportional to the diameter of the bullet. We should 
also note that GS is proportional to Ix 2 /I. This is why bench rest match bul- 
lets are short and light, which maximizes this ratio, and allows the use of a 
slow twist rate. As we saw in Chapter 9 minimizing the twist rate also mini- 
mizes the dispersion error due to CG offset. 

So what are the practical effects of GS on accuracy? Well it is important to 
realize that the bullet is traveling in a corkscrew motion about the trajectory 
when it is coning. In Figures 10-1 through 10-3 the coning angle at launch is 
about 0.2 degrees, which is likely to happen. For a 0.2 degree angle of attack 
the radius of the corkscrew motion will be about 0.009 inches for a GS of 
2.98. By the time the bullet reaches 200 yards the angular motion has damped 
so that the radius of the corkscrew motion is only 0.003 inches. For lower 
GS’s the radius of the corkscrew motion is even smaller. The reason for this 
behavior can be seen in the equation for the radius of the corkscrew motion. 

R = q * S * CLa * a * 12 / [(F2) 2 *m] 

R = radius of corkscrew motion, inches 

q = dynamic pressure, 1/2 * air density * V 2 . Sea level density = 0.00238 2 

slugs/cubic foot (0.0765 pounds/cubic foot) 

V = bullet velocity, fps 

S = bullet cross section area, ft 2 

CLa = slope of lift coefficient, varies from 2.25 for an 8 caliber ogive to 

3 for a 6 caliber ogive 

a = coning angle, radians. Radians = degrees/57.3 

F2 = slow precession frequency, radians/second. Varies from 64 cps 
at GS=2.98 to 127 cps at a GS of 1.13. 

m = bullet weight (pounds) divided by G (G=32.16 ft/sec 2 ) 


Chapter 10 : External Ballistics 

This equation agrees very well with 6DOF computer flight simulations. Notice 
that the radius (R) decreases with increasing slow precession frequency (F2) 
and since F2 increases with decreasing GS the radius will decrease rapidly 
with lower GS. In other words, the lower the gyroscopic stability the smaller 
the radius of the corkscrew motion. 

However, this is not the whole story. Note in Figure 10-4 (GS=1.13) that the 
coning angle jumped up to twice the initial angle of 0. 1 3 degrees and did not 
damp. As the GS gets smaller and closer to 1.0 the effect increases very 
rapidly and the projectile never damps. In special low GS cases (GScl.l) I 
have had bullets hit the target in a two foot circle. Some shooters are using 
6mm barrels with a 15 inch twist instead of the normal 14 inch twist. This 
will reduce the dispersion due to bullet CG offset by about 7% and may 
reduce your group size by as much as 5%-6% assuming that CG offset is the 
major cause of dispersion. It will also reduce the GS from 1.4 to 1.2 under 
normal conditions and the performance may be erratic under unfavorable 
atmospheric conditions. Under normal conditions the dispersion caused by 
the corkscrew motion by itself is too small compared to other error sources to 
worry about but can become an enormous effect at excessively low gyro- 
scopic stability factors (GS< 1.1). 

Recall that we tested the effect of muzzle blast pressure on in-bore bullet 
cant in Chapter 7, which is a much greater effect (0.2 inch radius of disper- 
sion for 0.2 degree bullet cant) and includes the effect of the corkscrew 
motion. The muzzle blast error was due to the muzzle blast pressure causing 
a lateral drift velocity and had little to do with the corkscrew motion. How- 
ever, the test in Chapter 7 was run with a GS of 1 .6 and I am sure that the 
muzzle blast effect would have been greater with a lower GS. So GS gets in 
the act and effects dispersion even at close range. 

Some of the things that can cause an initial angle of attack the instant that the 
bullet exits the muzzle are in-bore bullet cant, bullet base cant, defect in the 
bore at the muzzle, and possibly powder combustion products lying in the 
bottom of the bore. However, bear in mind that the muzzle blast effect is 
much greater than the corkscrew motion effect that occurs after the bullet 
leaves the transitional ballistics region at the muzzle. After the bullet leaves 
the muzzle area there are other disturbing factors that can effect the bullet 
and introduce an angle of attack and coning motion. A cross wind of 20 mph 
will cause an initial angle of attack of about 0.5 degrees which will produce 


Rifle Accuracy Facts 

a coning motion. At a low GS this initial angle of attack can grow by a factor 
of two or more. If the cross wind component remains constant from shot to 
shot there will be no effect on dispersion. However, if you shoot in variable 
conditions and hold off to correct for wind drift there will be dispersion in 
addition to the usual wind drift error. The dispersion may be in any direction 
and not necessarily in the horizontal direction. This error can be larger than 
those discussed earlier but there is no simple way to evaluate it. There are 
just too many variables, but a high GS will help. A single tiny rain drop can 
cause the bullet to rotate to a high angle of attack and result in a significant 
flyer. Just how bad the flyer will be depends on the size of the drop and 
where it strikes the bullet. The probability of a bullet hitting a rain drop 
depends on the density of the rain drops and the length of the trajectory, but it 
does happen. 

The optimum situation is to maintain a GS of 1 .4 or greater at a minimum 
spin rate. If one could move the CG further forward for a given bullet shape 
this would reduce Ma and increase GS. Back in the 1960’s I made a 270 
bullet with a 150 grain jacket stable at slow twist rates by moving the CG 
forward. A plastic cylinder was inserted into the base of the jacket and the 
lead core swaged on top of it (see Figure 10-10). This configuration moved 
the CG forward with respect to the center of pressure and the bullet was 
stable in a 16 inch twist barrel. A 150 grain 270 bullet normally requires a 10 
inch twist. Consequently, the error due to CG offset was reduced by about 
38%. While the accuracy improved in firing tests the accuracy wasn’t as 
good as I had hoped, because the jackets had excessive run out. The 270 
bullet weighed about 100 grains so the ballistic coefficient was reduced. This 
idea might be worth pursuing using 6mm match grade jackets and a twist slower 
than 14 inches for benchrest competition. For the moment a 6mm 68 grain match 
bullet at 3200 to 3300 fps with a 14 inch twist is about as good as you can do. 

Figure 10-10- Photograph of a 270 bullet with a light plastic cylinder swaged into 
the rear of the jacket behind the lead core. This moved the CG forward enough so 
that the bullet was stable in a 16 twist barrel. This jacket would normally result in a 
150 grain bullet, but this bullet weighed 100 grains with the plastic insert. 


Chapter 10 : External Ballistics 

Figure 10-11 - Sketch showing how aerodynamic drag acting along the flight path 
actually causes wind drift rather than the wind blowing on the side of the bullet. 

Wind Drift 

Everyone knows that bullets will drift downwind in a horizontal direction but 
many people don’t understand how the drift takes place. Horizontal wind 
drift is not caused by the wind blowing against the side of the bullet. When a 
bullet is launched it heads into the wind and the drift is caused by the drag 
force acting on the bullet, which is canted with respect to the flight path (see 
Figure 10-11). This sketch shows how the bullet starts out at the muzzle and 
very quickly aligns itself with the relative wind vector so that the angle of 
attack approaches zero with respect to the wind vector. In a 20 mph cross 
wind the centerline of the bullet will be canted at an angle of 0.52 degrees 
with respect to the flight path. An angle that small or even larger is difficult 
to detect from distortion of bullet holes. It takes less than one fast precession 
cycle for the bullet to align itself to the relative wind vector and reduce the 
angle of attack due to the wind to near zero. When there is no wind the bullet 
geometric axis lines up with the flight path and the drag force also is lined up 
with the flight path and there is no wind drift. So, wind drift is not caused by 
the wind blowing on the side of the bullet as many people think. 

A lively discussion recently took place in “Precision Shooting’’ on how the 
vertical component of wind drift must be due to Magnus force. Since I am 
very familiar with Magnus effects (Reference 25) I wrote an article that 


Rifle Accuracy Facts 



Figure 10-12- Plot of computer flight simulations of wind drift for three different 
gyroscopic factors (GS). The drift angle is apparent. The plot is for a right hand twist 
and the direction of the vertical component would be reversed for a left hand twist. 

appeared in the November 1994 issue of “Precision Shooting” explaining 
that Magnus force acts in the wrong direction and is much too small to cause 
the observed effect. People also insist on blaming the vertical wind drift 
effect on rifling marks rotating in a cross wind. Aside from the fact that this 
would result in just the opposite effect from that which is observed, the ri- 
fling marks are buried in a boundary layer that is several times thicker than 
the depth of the rifling marks. The boundary layer is a thin layer of slowly 
moving air that forms on the surface of the bullet as a result of air viscosity. 
This boundary layer tends to blur the effect of small surface irregularities 
such as rifling marks. Instead of Magnus effects causing the vertical wind 
drift component it is caused by gyroscopic moments similar to the yaw of 
repose that we just discussed. Figure 10-12 shows how a 68 grain 6mm 
bullet will drift in the wind for three different gyroscopic stability factors 
(GS) as determined from 6DOF computer flight simulation. You can see that 
the more gyroscopically stable the bullet is, the larger the vertical wind drift 
component. Table 13 shows the calculated wind drift data in tabular form for 
both 100 and 200 yards. The data are calculated for a 68 grain 6mm match 
bullet with a gyroscopic stability factor of 1.5 in a 14 inch twist barrel. 


Chapter 10: External Ballistics 



Calculated Wind Drift Data 




100 yards 

10 mph 

20 mph 

200 yards 

10 mph 

20 mph 















You can see that the horizontal drift component is roughly proportional to the 
wind velocity and proportional to the square of the range while the vertical 
component is roughly proportional to both the wind velocity and range. 

Figure 10-13 shows a target that resulted from firing a 6BR rail gun at 3200 
fps (200 yards) with Berger 68 grain match bullets (14 inch twist) in a wind 
of varying intensity from the right, and you can see the vertical and horizontal 

Figure 10-13 - An 
enlarged plot of a 
target where 5 
shots from a 6mm 
rail gun were 
fired at 200 *p 
yards. The wind I / 
was from the 
right and 
varied in 
intensity. The 

gyroscopic stability factor can be 
determined by measuring the wind drift 
angle of 17 degrees and then obtaining the 
GS from Figure 10-14. In this case the GS turned out to be 1.60 for this 68 grain 
bullet with a 14 inch twist at 5000 feet altitude. At sea level the GS would be 1.38 
when corrected for the higher density at sea level. 


Rifle Accuracy Facts 

Figure 10-14 - Graph showing how the drift angle varies with gyroscopic stability 
factor (GS). 

component of wind drift. If you measure the angle between a line through 
the bullet holes and a horizontal line, the angle turns out to be about 17 de- 
grees. If you look at Figure 10-14, which is a plot of the vertical drift angle 
as a function of GS, you can see that the data in Figure 10-13 (17 degrees) 
gives you a GS for this particular 68 grain 6mm match bullet of 1 .60. If you 
correct this value for the fact that the test was run at high altitude (5000 feet) 
using Table 12 (divide by 1.1605) the GS at sea level would be 1.38 which is 
adequate stability. So, if you are curious about how stable your bullets are 
you can run this simple test and use Figure 10-14 to find out. It is valid at any 
range or velocity. You have to fire when the wind is gusting and that way you 
can get shots at varying wind velocity. The direction of the vertical compo- 
nent of wind drift will reverse with a left hand twist barrel. 

Everyone is aware of the fact that bullets drift with a cross range wind. The 
question is — how much. The most convenient way to determine wind drift is to 
look it up in tables, such as those in Sierra’s reloading manuals. However, if you 
want to calculate it yourself there is a simple equation that gives good results. 

Chapter 10: External Ballistics 

Figure 10-15 - Photograph showing two types of wind indicators (wind flags) 
commonly used by bench rest shooters. They are both weather vanes which indicate 
the direction of the wind that have ribbons attached to the tails to indicate wind 
velocity. The wind indicator on the left has a propellor as another velocity indicator. 

Horizontal wind drift = 0.00827 * (v/Va) * (R I 2 /BC), at SL 

v = cross range wind velocity in miles/hour 
Va = average bullet velocity over the range in fps 
R = range in yards 
BC = ballistic coefficient 
SL = sea level altitude 

I compared this equation with a 6DOF computer simulation for a 150 grain 
270 bullet at 400 yards with a 10 mph cross wind and the equation gave 6.96 

inches of drift compared to 6.76 inches for the 6DOF calculation (error = 
2.8%) at an altitude of 5000 feet. You can use the density correction in Table 
12 to correct for altitude. Just divide the result of the drift equation by the 
density factor. This equation is useful in that it shows that wind drift is di- 
rectly proportional to wind velocity and the square of the range, while it is 
inversely proportional to the bullet velocity and ballistic coefficient. This 
means, of course, that one should maximize muzzle velocity and ballistic 
coefficient for minimum wind drift. 


Rifle Accuracy Facts 

Wind drift is an important factor in both hunting and target shooting. Having 
collected most of the North American big game species, including a Grand 
Slam in sheep, I can appreciate the effect of wind drift in hunting accuracy. 
The calculations made above were for a 270 Weatherby wild cat cartridge 
(sharp shoulder) that is my favorite hunting rifle. What I do is memorize the 
fact that the particular bullet that I am using will drift about 7 inches at 400 
yards in a 10 mph wind. Out to 200 yards I don’t worry about wind drift 
(1.75 inches). However, I once had to shoot an elk at 450 yards in a 30 mph 
wind so I quickly multiplied 3 times 7 in my head and aimed about 2 feet to 
the right. It hit the elk within a few inches of where I wanted to place the 
bullet. As a result I had a once in a lifetime trophy that was number 1 3 in the 
book. Without that information and a bit of luck, I probably would have 
missed. The moral of the story is that you hunters had better pay attention to 
wind drift. 

Benchrest shooters and long range target shooters go to a lot of trouble to 
“dope the wind”. A calculation using the drift equation for a 68 grain 6mm 
Berger match bullet at 3200 fps tells us that the drift at 200 yards will be 3.75 
inches for a 10 mph cross wind (or about 1 inch at 100 yards). Well I think 
you can see that if you are trying to shoot small five shot groups (under 0.5 
inches) in a match at 200 yards in windy weather, the wind can be a real 
problem. Figure 10-15 shows two wind indicators commonly called wind 
flags that were made by Don Nielson (8 1 8-883 5866). The one on the right is 
essentially a weather vane with a ribbon attached to the tail. The one on the 
left is the same thing with a propellor on the front of the vane. Typically, 
three or more wind vanes are placed between the shooter and the target. The 
trick is to watch the weather vanes for wind direction and to watch the rib- 
bons or the propellor for wind velocity. The problem is to mentally process 
the six pieces of data and decide when and where to shoot. Some people get 
very good at doing this instinctively, but it takes a lot of practice. All this 
mental exercise makes my head hurt, so I built the electronic device shown in 
Figure 10-16 that does all this mental stuff for you. 

The electronic device was originated by Walter Watts (Reference 26) in the 
late 1960’s and he won several big benchrest matches with it. But I don’t 
think it was ever produced commercially. I built it originally to try to mini- 
mize wind effects in diagnostic testing before I built the Tunnel Range and it 
helped. The swiveling vanes are only sensitive to the cross range wind com- 
ponent because they are turned so the plane of the vanes is parallel to the 


Chapter 10: External Ballistics 

bullet trajectory. The vanes on the 
electronic gage are mounted on the 
shaft of a 1 0 turn 20,000 ohm po- 
tentiometer, which forms two arms 
of a resistance bridge. The bridge 
is powered by C cell batteries. A 
two wire cable connects all three of 
the gage outputs in parallel to an 
indicator meter on the bench 
(Figure 10-17). There are three C 
cells (4.5 v) in the gage nearest the 
bench, two cells (3 v) in the middle 
gage and one cell ( 1 .5 v) in the gage 
near the target. This automatically 
provides weighting factors of 3/6, 
2/6, and 1 /6 for the outputs of the 
three gages. The theory is that the 
wind drift over the first 1/3 of the 
trajectory will be 1 .5 times that of 
the second 1/3 of the range and 3 
times the drift over the remaining 
1/3 of the range. The three gages 
are placed at 17, 45, and 77 yards 
from the bench for a 1 00 yard tar- 
get. This spacing is approximately 
the midpoints of the three 33.33 
yard intervals in range. According 
to 6DOF computer calculation this 
method of correction is quite good. 
The indicator on the bench 
(Figure 10-17) is a small box with 
a microammeter that indicates both 
plus and minus 50 (lamps. When the 
wind is from the right the needle 
moves to the right and vice versa. 
There is an amplifier in the box that 
allows you to balance the meter and 
adjust the sensitivity. The sensitivity 

Figure 10-16- Photograph of an electronic 
wind indicator which provides an electrical 
output proportional to the cross wind velocity 
component. The vane surface is placed 
parallel to the bullet trajectory so that it is 
sensitive to the cross range wind component. 
Three of these gages are used and are 
connected by a cable to the indicator on the 
bench shown in the next figure. 

Figure 10-17 - Photograph of the indicator 
on the bench for the electronic wind gages. 
When the wind is from the right the meter 
needle moves to the right and just the 
opposite for a wind from the left. The goal is 
to fire when the needle is in the same place. 



Rifle Accuracy Facts 

can also be adjusted by raising or lowering the aluminum arrow shafts that 
hold the vanes relative to the pivot point. The way you use this device is to 
observe where the meter needle is pointing most of the time and try to shoot 
when the needle is at your chosen value. Once in a while you will get caught 
when the wind suddenly dies off or persists at a higher value and you will 
have to aim off to correct for the change in drift. However, you can calibrate 
the effect for a change in conditions on this device by firing on the sighter 
target. I prefer to use the free recoil method of shooting where the gun is 
fired by only touching the trigger while the gun sits on the sandbag rests. 
With the firm hold method I find it difficult to watch both the meter and the 
scope at the same time. The batteries in this device last a long time (years) 
and are no problem. The problem with this device is that you have to string 
77 yards of cable (or twice that length for a 200 yard match), which is a real 
nuisance even when it is on a reel. Obviously one could use radio links to get 
rid of the cable, but this is not a trivial problem and battery life becomes a 
big problem. 

People seem to exaggerate the effect of tail winds or head winds. Intuitively 
you would think that a head wind would slow the bullet down and make it 
impact at a lower point. It does, but the effect is much less than most people 
think. A 6mm 68 grain bullet at 200 yards will strike low by 0.017 inches for 
a 20 mph headwind or 0.017 inches high for a 20 mph tailwind. The time of 
flight at 200 yards varies by ±0.4 msec. Now a good 200 yard bench rest 
group is 0.3 to 0.4 inches in calm weather so I don’t think that 0.017 inches 
for a 20 mph variation in head or tail wind is significant. The effect at 100 
yards is less than half the 200 yard effect (±0.007 inches). There is one 
exception to all this and that is the effect of tail or head winds blowing over 
obstructions behind or in front of the shooter. On our range I have noted 
vertical dispersion that I think comes from the downwash created by a tailwind 
blowing over the roof that covers the benches. This could be minimized by 
building an electronic gage that is sensitive to vertical wind components. We 
are also certain that head or tail winds blowing over berms between the bench 
and target causes vertical dispersion. 

We have shown the effect of ballistic coefficient (BC) on wind drift, so it is 
appropriate to discuss ballistic coefficient. 


Chapter 10: External Ballistics 

Ballistic Coefficient 

Ballistic coefficient (BC) is simply a numerical value that expresses the ratio 
of weight to drag for a given projectile. The drag is proportional to the drag 
coefficient (Cd) and the cross section area which varies as the square of the 
diameter of the bullet. The ballistic coefficient is 

BC = 0.0000714 * W / (D 2 * Cd) * o 


W = bullet weight in grains 

D = caliber in inches 

Cd = drag coefficient 

<7 = air density factor from Table 1 2 

and the constant takes care of the units involved in the equation. The drag 
coefficient varies with Mach number (velocity and temperature) and must 
either be obtained from experiment or theoretical calculation. A sample cal- 
culation of BC for a 150 grain 270 bullet goes like this 

BC = 0.0000714 * 150 / (0.277 2 * 0.30) = 0.465 

where the bullet is a flat base tangent ogive cylinder with a soft point tip. The 
drag coefficient was taken from wind tunnel data. 

The next thing to do is to find out how to estimate the drag coefficient. One 
easy way is to get the BC from the manufacturers and rearrange the equation 
for BC so that you can solve for Cd. 

Cd = 0.0000714 * W / (D 2 * BC) * c 

For instance Walt Berger quotes a BC value of 0.276 for his 68 grain hollow 
point 6mm match bullet at 3000 fps. Consequently, 

Cd = 0.00007 14 * 68 / (0.243 2 * 0.276) * 1 = 0.298 

This Cd seems about right compared to experimental data in Figure 10-18, 
which makes the BC seem reasonable. This bullet is a small flat base hollow 
point that has a very small tip diameter. 


Rifle Accuracy Facts 

Figure 10-18- Experimental data showing the effect of nose shape and Mach 
number on aerodynamic drag at zero angle of attack. Shapes 1 and 2 have tangent 
ogive noses 2.5 calibers in length, but shape 2 has a blunt nose typical of soft point 
bullets. Shape 3 has a 3.5 caliber length tangent ogive. Cylindrical afterbody length 
has only a small effect on drag. 

The experimental drag coefficients that have been plotted for three different 
bullet shapes in Figure 10-18 were taken by O. Walchner in Germany during 
WWII (1939). I chose to show it to you because I wanted you to know that 
this kind of data has been around for a long time. Bullet #1 is a 5 caliber 
tangent ogive cylinder with a nose length of 2.5 calibers and a sharp tip. 
Bullet #2 has the same shape except the nose tip has been rounded off so that 
it is similar to soft point commercial bullets. Bullet #3 has a sharper nose 
that is 3.5 calibers long instead of 2.5 calibers. You can see that the sharper 
the tip and the longer the ogive the lower the drag. The drag of modern 
commercial bullets with the sharp-pointed ballistic tips is close to the drag of 
bullet #1. So, you can see that the BC of the ballistic tip bullets can be as 
much as 25% greater than the usual soft point. 

Bullet #3 is typical of the very low drag bullets that have recently become 
available, except that they usually have a short boat tail. The boat tail does 
reduce the drag at low Mach numbers and becomes important at ranges over 


Chapter 10: External Ballistics 

500 yards. It has a negligible effect at high Mach numbers and short range 
(out to 300 yards or so). These long bullets with boat tails are difficult to 
stabilize and require high twist rates. As a result of the high twist rates and 
short rifling engraving length, they may be subject to core slippage with soft 
cores. If this happens the accuracy will be poor. The short engraving length 
can also increase the tendency for the bullet to tip in the bore. 

The effect of bullet afterbody length on drag is very slight. The main effect 
at high velocity is the shape of the nose as a result of the high pressure acting 
on the nose. Most of the rest of the drag is caused by the low pressure in the 
wake acting on the base. The ratio of the head drag to base drag at 3000 fps 
is 2 or 3 to 1 . At lower velocities the base pressure becomes more important 
relative to the head or form drag and this is why a boat tail becomes more 
effective at lower velocities or Mach numbers. The skin friction drag devel- 
oped in the boundary layer is less than 5 percent because of the laminar bound- 
ary layer. The effect of rifling marks on drag has been tested and found to be 
small. The reason is that the rifling depth is only 2 or 3 mils and is buried in 
the boundary layer. Also, the rifling marks are tangent to the free stream 
velocity until the bullet slows down. The spin rate slows to some extent but 
not nearly as fast as the flight velocity. 

There is a lot of aerodynamic data available on projectiles but you usually 
have to have a connection with the military to get access, even though it is 
unclassified. For instance. Reference 27 published by BRL has aerodynamic 
data on over 100 projectiles. I think the average shooter is better off either 
just measuring the BC or accepting the BC published by manufacturers in- 
stead of trying to obtain drag coefficient data. 

Measuring the BC is really a simple process if you have a chronograph. All 
you need to do is measure the velocity near the muzzle and the velocity at the 
range you want to cover. Several shots should be fired and the average ve- 
locities should be used in the calculation. Figure 10-19 shows the result of 
an experimental measurement of velocity at 0, 100, 200, and 270 yards plot- 
ted on a semi-log scale. A fundamental equation can be derived that allows 
calculation of Cd from this data. It is 

Cd = 0.9221 * W * ln( Vi/Ve) / (D 2 * R * a) 

Rifle Accuracy Facts 


W = bullet weight in grains 
Vi = initial velocity in fps 
Ve = end or final velocity in fps 
In = natural logarithm to base e 
D = caliber in inches 
R = range in feet 

o = density factor shown in Table 1 2 

So taking the start and final velocities from the figure 
where R=300 yards, we get 

Cd = 0.9221 * 180 * ln(30 10/25 10) / (3.085 2 * 900 * 1.1605) 

Cd = 0.303 

If you look at Figure 10-18 at a Mach number of 2.4, which is the average 
Mach number over the 300 yard range, you can see that this Cd is about right 
for a 180 grain Remington bronze point bullet. You can also get BC from 

BC = 0.00007143 * W / (D 2 * Cd) * a 


BC = 0.00007143 * 180 / (0.3085 2 * 0.303) * 1.1605 = 0.517 

This is a reasonable BC compared to other sources. The function In is the 
natural log of the number in parentheses and can be found on most hand 
calculators. The data were plotted on a natural log scale in Figure 1 0- 1 9 to 
show that the equation involving the log function is indeed correct, because 
the data plot as a straight line. This method gives you a simple way of mea- 
suring Cd and BC over any range that you desire. Remember the Cd that you 
get is nondimensional and depends only on the Mach number. BC depends 
on Mach number and air density. Many people think that the BC is greatly 
effected by angle of attack but it isn’t in a normal situation. Figure 10-20 
shows what is called a drag polar for a typical ogive cylinder bullet with a 
sharp nose. It shows how the drag coefficient varies with angle of attack. You 
can see that the drag coefficient increases by only a small amount (less than 
1%) at an angle of attack of 1 degree. Back in Chapter 7 we found that the 
angle of attack at muzzle exit was less than 0.5 degrees on a short 270 bullet. 


Chapter 10 : External Ballistics 

30 CAL 

^3010 5000 FEET ALTITUDE 

„ 3000 * 










256 O- I * 3 *-^ 


ro ft 

o u 

O C 

° 5 

Cd = .3' 


BC = .517 

100 200 300 


Figure 10-19 - Experimental 
method of determining drag 
coefficient and ballistic 
coefficient. The velocities at 
0, 100, 200, and 270 yards 
were measured on a 180 
grain Remington Bronze 
Point bullet and plotted on a 
semilog graph to show the 
logarithmic dependence of 
velocity on range. The drag 
coefficient can be calculated 
from a simple equation 
shown in the text. 

Figure 10-20 - Graph 
showing how the aerody- 
namic drag on an ogive 
cylinder bullet varies 
with angle of attack. The 
aerodynamic drag is very 
insensitive to small changes 
in angle of attack. From the 
tests in Chapter 7 we know 
that the angle of attack at 
muzzle exit is much less than 
one degree. A one degree 
angle increases the drag 
coefficient and decreases 
the ballistic coefficient by 
less than one percent. 

The geometry of most bullets simply won’t permit large launch angles at the 
muzzle. If the coning angle is greater than 1 degree it is unstable and BC is 
the least of your concerns. 

I think too much has been made of ballistic coefficient in general. It is 

important at long range and there you should use a heavy bullet for the cali- 
ber at high velocities with a sharp nose and a boat tail. A high BC will 

minimize wind drift and vertical dispersion due to gravity drop variations. 
However, it has little effect at 100 or 200 yard ranges where most bench rest 
matches are fired. In both cases bullet CG asymmetry is more important. 


Rifle Accuracy Facts 

Gravity Drop 

One accuracy problem that generally isn’t appreciated is the effect of varia- 
tions in muzzle velocity on gravity drop, which causes vertical dispersion. 
This effect can be calculated with a simple equation. 

8GD = 385.92 * R 2 * 8V / (Va A 3), inches 


8GD = the difference in gravity drop due to a difference in 
muzzle velocity 

R = range in feet 

8V = change in velocity, fps 

Va A 3 = average velocity over the range cubed 

The average velocity over a given range can usually be gotten from a reload- 
ing manual. Suppose we have an extreme spread of 30 fps in a 5 shot group 
at an average velocity of 3000 fps. Then the vertical dispersion due to varia- 
tion in gravity drop at 100 yards will be 0.039 inches. At 200 yards the 
vertical dispersion will be about four times that at 100 yards or about 0.16 
inches. If you are trying to shoot a 0.2 inch group at 100 yards an error of this 
size is significant. Another way to estimate this error if you know the total 
gravity drop at a given range is 

8GD = 2 * GD * 8V / Va 

The total gravity drop (GD) can usually be found in some reloading manuals. 
For instance from the Sierra manual a 70 grain 6mm HP fired at 3 1 00 fps has 
a total gravity drop at 100 yards of 1.90 inches. For this case the dispersion 
error for an extreme spread of 30 fps in muzzle velocity is 

GDe = 2 * 1 .90 * 30 / 3000 = 0.038 inches 

which agrees well with the other equation. A 180 grain spitzer boat tail bul- 
let fired at 3200 fps will have a gravity drop error as much as 5 inches at 1 000 
yards for a 8V of 30 fps. The reason for this is the gravity drop at 1000 yards 
is more than 100 times the drop at 100 yards. The gravity drop goes roughly 
as the square of the range. 


Chapter 10 : External Ballistics 

Obviously, the only control we have over this error is to strive for a minimum 
extreme spread in velocity. About the best that I can do on the average is 15 
to 20 fps, which really isn’t good enough. As we saw in Chapter 2 filling up 
the case with powder helps but you may run into excess pressures. Reaming 
primer flash holes also helps. Some brands of primers seem to do better than 
others with a particular powder and case. I think that to be competitive in 
match shooting it is essential to have a chronograph. 

Fortunately there is a way to compensate for the velocity variation error. We 
covered this under Special Bench Rest Gun Problems at the end of Chapter 4 
but it may not have been obvious to the reader. If you refer back to Figures 4- 
39 and 4-41 you can see that the vertical impact point varies as a sine wave 
with changing muzzle velocity. This is due to barrel vibration and will be 
different for different guns because the frequency of the vibration will be 
different. If you shoot at an average velocity that is near a peak and on the 
negative slope the impact point will be slightly lower for a higher than aver- 
age velocity and slightly higher for a lower than average velocity. This will 
compensate for the variation in velocity. These points correspond to 3080 
fps and 3330 fps on Figure 4-41 . This particular heavy varmint rifle built by 
custom gunsmith Jim Borden has a Stolle action with a barrel length of 21.5 
inches from the front of the action to the muzzle. The problem here is that 
the optimum low velocity point (3080 fps) requires an excessively light load 
which might cause increased velocity variation and the optimum higher ve- 
locity load point (3330 fps) causes excessive case expansion and may cause 
core stripping due to the higher chamber pressure. If the barrel were shorter 
the frequency would be higher and the sine wave would shift to the left. In 
that case the positive peak could occur at a more optimum load and velocity 
(3200 fps). The velocity region between the negative and positive peaks is 
the worst place to shoot because the barrel vibration accentuates the effect of 
variations in velocity on gravity drop. 

Velocity Measurement 

I became interested in measuring bullet velocities in 1949 and built my first 
chronograph in 1950. A chronograph works by counting the number of pulses 
generated during the time interval it takes for the bullet to trigger the start 
gate and trigger the stop gate. The pulses are generated by a crystal 


Rifle Accuracy Facts 

Figure 10-21 - Early 
chronograph built 
by the author in 
1950. It used tube 
technology and 
was patterned after 
the original Potter 
chronograph. It 
required 1 10 volt 
AC power. 

controlled oscillator running at a very precise frequency and the pulses are 
counted by a series of decade counters. This idea was certainly around in the 
1940 s and perhaps earlier. I believe the first man to use this idea was named 
Potter and the first chronographs were named after him. My first chrono- 
graph (Figure 10-21) was essentially a Potter chronograph using vacuum tube 
technology and contact screens. The only problem was that it required 120 
vac power. Since you had to plug it in somewhere its usefulness was limited. 
However, it still works after 48 years and I occasionally use it for other pur- 
poses. In 1962 transistors became available and I enlisted the aid of an elec- 
trical engineer friend of mine (Harold Bennett) and we built a transistorized 
version of the original Potter counter (Figure 1 0-22). It was battery powered 

Figure 10-22 - Transistorized battery powered chronograph built by the author in 
1962. A contact screen is shown which has aluminum foil cemented to both sides 
of apiece of cardboard. When a bullet passes through the screen it completes the 
electrical circuit between the aluminum foil conductors triggering the chronograph. 


Chapter 10 : External Ballistics 

Figure 10-23 - Photograph of a modern state-of-the-art chronograph (Oehler35P) 
with three optical gates. This chronograph uses electronic chip technology for 
computation and has a built in printer that records all the data. It measures velocity 
within 2-3 fps at 3000 fps. The optical gates are much more convenient than other 
types of triggers. 

and also used contact screens for gates. One of these contact screens is shown 
in Figure 10-22. Both of these chronographs had clock speeds of 100 kc 
which limited the resolution to 0.5% (see Figure 2-18). This is adequate for 
most purposes but not as good as one should have for diagnostic work. Mod- 
ern chronographs have a resolution of better that 0.1% with a 6 foot screen 
spacing. The contact screens are simply a piece of cardboard with aluminum 
foil glued to both sides. When a bullet passes through the screen it completes 
an electrical circuit starting the chronograph. These are very accurate gates, 
but have the disadvantage of not allowing accuracy testing at the same time 
because they are opaque. Anyhow, I did a lot of work with these instruments 
in the 1950’s through the 1970’s. 

Modern chronographs, such as the Oehler 35P (Figure 10-23), work the same 
way, except that they use a faster clock frequency (4 megacycles) and have 
solid state chip electronics for less battery drain. They also have built in 


Rifle Accuracy Facts 

printers and use optical gates that depend on sunlight or electric lights to 
trigger the counter. In addition they indicate the maximum and minimum 
velocity, average velocity, extreme spread in velocity, and standard devia- 
tion. In the old days we had to compute all this stuff, so things are much 
faster and easier these days. However, standard deviation is an overkill as far 
as I am concerned and is meaningless in a small sample (i.e., less than 30 
data points). Standard deviation will usually range between 40 and 45 per- 
cent of the extreme spread in a 5 shot group. The quantities that are mean- 
ingful are average velocity and extreme spread in velocity. The Oehler 35P 
has three optical screens and it measures the velocity between the first and 
second screen and between the first and third screen. If the difference be- 
tween these two velocities is excessive it warns you by printing an asterisk 
next to the doubtful data. The Oehler chronograph is the best chronograph 
that I have used and I believe it to be entirely adequate. 

The only problem that I have had with the Oehler chronograph is that it is 
sensitive to elecromagnetic radiation from a radar situated at an airport about 
a mile away from our range. We found that we could solve the problem by 
parking a vehicle between the radar and the chronograph. This undoubtedly 
is a very unusual situation that would rarely be encountered. Glint is another 
problem with any chronograph that has optical gates. Glint occurs when 
light is reflected from the ground or some place else onto the bottom of the 
bullet which can erratically trigger the optical gates. I paint the tube (rail) 
that the gates are mounted on with flat black paint and put a dark tarp on bare 
ground to reduce the reflectivity. Glint problems can be difficult to detect, 
but I have definitely seen it happen when operating on bare sandy soil. Oehler 
also sells light bulbs that mount on top of the diffusers on the gates for opera- 
tion in dark conditions. I use these in the Tunnel Range where it is dark and 
they work very well. However they do require 120 vac power. I prefer a 
screen spacing of six feet which gives you a measurement precision of 2-3 
fps without the length becoming too unwieldy. 

The army experimented with several methods of triggering gates including 
magnetic, capacitance, and optical (called skyscreens). They were all dis- 
carded in favor of radar sometime in the 1970’s because of the extreme prob- 
lems with muzzle blast. The orange colored translucent light diffuser mounted 
above the photodiode (Figure 10-23), that was originated by Oehler, was a 
big improvement in optical gates. 


Chapter 10 : External Ballistics 

You will see two terms used in measuring velocity - muzzle velocity and 
instrumental velocity. Instrumental velocity is the projectile velocity mea- 
sured at some distance from the muzzle while muzzle velocity is the velocity 
near the muzzle after leaving the muzzle blast region (10-20 calibers). Muzzle 
velocity is the instrumental velocity corrected for the loss in velocity be- 
tween the muzzle and the center of the chronograph gates. If you want to get 
“picky” about this you can estimate the velocity change between the muzzle 
and the chronograph velocity from 

ctV = 1.461 *V*D 2 *R*Cd/W 


gV = change in velocity, fps 
V = measured velocity, fps 
D = caliber, inches 

R = distance from muzzle to the center between gates, ft 
Cd = drag coefficient 
W = bullet weight, grains 

For instance, for Cd = 0.3, V = 3200 fps, D = 0.243 inches, W = 68 grains, 
and R = 8 feet, oV comes out to be 9.7 fps velocity loss. Add that value to the 
chronograph velocity and you have muzzle velocity. 

Since I have already told you more about measuring velocity than anyone 
ever wanted to know, we consider the effect of rifle cant on accuracy. 

Rifle Cant 

Rifle cant means rotating the rifle about the bore axis. If the rifle cant angle 
varies it can have a serious effect on accuracy - particularly horizontal dis- 
persion. I think you can visualize the problem if you consider firing a rifle 
that is sighted in to hit the aim point so that the sight is adjusted upwards to 
compensate for the bullet gravity drop. If you were to fire the rifle in the 
inverted position you would not only have the drop due to the sight compen- 
sation but the gravity drop added to it. Consequently, the bullet will strike 
low by the equivalent of twice the gravity drop. Just to prove this concept 
I ran an experimental test. 


Rifle Accuracy Facts 

22 LR, 50 YARDS 









Figure 10-24 - Computer plot of a target showing four groups fired with the rifle 
vertical, canted 90° clockwise, inverted, and canted 90° counter clockwise. 

A 22LR rifle was fired with a cant of 0°, 90° right, 90° left and inverted at a 
range of 50 yards. Four shot groups were fired at each cant angle and the 
results are plotted in Figure 1 0-24. The muzzle velocity and the velocity at 
the target were measured so that the bullet gravity drop could be accurately 
computed. You can see that a circle with a radius of 3.8 inches can be drawn 
through the four groups. Well, I was surprised, because the calculated bullet 
drop is only 2.7 inches! So where is the extra 1.1 inches coming from? It 
turns out that the barrel droop due to gravity causes an additional 1 . 1 inches 
of drop that must be compensated for by the scope sight. The barrel in the 
test rifle was a slender cylinder and very flexible. Barrel droop can be calcu- 
lated very accurately on a cylinder but I won’t go into detail because most 
barrels are much stiffen So, I felt that this was adequate proof of the concept. 

The error can be calculated from two simple equations. 

Horizontal error = bullet gravity drop * Sine(cant angle) 

Vertical error = bullet gravity drop * (l-Cosine(cant angle)) 


Chapter 10: External Ballistics 

For small angles (less than 10°) these equations can be simplified to 
Horizontal error = GD * O / 57.3 

GD = bullet gravity drop, inches 
O = rifle cant angle 

and the error is in inches. The vertical error is too small to worry about at 
small angles. 

An example is the GD on a 68 grain flat base 6mm bullet at 200 yards is 
about 7.93 inches with a muzzle velocity of 3200 fps. The horizontal error 
for a 0.1 degree rifle cant will be about .014 inches or about 0.14 inches for a 
1 degree cant. This means that you have to worry about rifle cant in the 
bench rest game if you can’t keep your rifle aligned better than 1 degree. At 
1000 yards this effect becomes serious. The bullet gravity drop on a 300 
Weatherby with a 200 grain bullet fired at 3000 fps will be about 296 inches 
at 1000 yards. Therefore, a 1 degree cant will give you a 5.2 inch horizontal 
error. Since people who win these 1000 yard matches shoot 6 inch groups 
you really have to be careful about rifle cant. 

Hunting is another place where rifle cant can have a significant effect, prima- 
rily because you often don’t have a good vertical reference in mountain ter- 
rain. Suppose you try to hit a big game animal at 300 yards with a 270 130 
grain bullet at 2900 fps and you cant the rifle 10 degrees. You will miss your 

aim point by 3.7 inches. At 500 
yards you will get more than three 
times that amount or about a foot. A 
ten degree cant angle is fairly easy 
to have happen in rough country - at 
least in my experience. So, while 
not as serious as wind 
effects, the rifle cant effect is 
large enough to take seriously at 
long range. 

Figure 10-25 shows a bubble level 
device mounted on a scope that is 

Figure 10-25 - 
Anti-cant level 
device mounted on 
the barrel of a 36 power 
Bausch and Lomb target 
scope just ahead of the eyepiece. 
It is effective in minimizing 
rifle cant. 


Rifle Accuracy Facts 

extremely sensitive to cant angle. It is easy to hold the cant angle to less than 
0.1 degree with this device, which is manufactured by DHB Products (phone 
number l-(703)836-2648). This is about the only way that I know of mini- 
mizing this error at long ranges. At short ranges in target shooting you can 
sight in the rifle so that the bullet impacts at a distance equal to the gravity 
drop below the aim point. This amounts to 1 .9 inches at 100 yards and about 8 
inches at 200 yards for a 68 grain 6mm match bullet at 3200 fps. If you follow 
this procedure you will effectively eliminate the effect of rifle cant. 

Bullet Shape Asymmetries 

Bullet tip deformation is one problem in external ballistics that has been ex- 
plored unsuccessfully in the past. The reason for this is that the effect is so 
small it is not detectable in experimental tests. However we can estimate the 
error by running trajectory simulations with the 6DOF computer code. 



Figure 10-26 - Drawing of a 270 150 grain soft point bullet with a mutilated nose 
simulated by slicing it off at a 45 degree angle. This type of deformity is not unusual 
in magazine fed magnum big bore rifles using exposed lead bullet tips. 

Figure 10-26 shows a drawing of a 270 1 50 grain bullet with an exposed lead 
soft point that has been deformed by cutting off the tip at a 45 degree angle. 
The results of the trajectory simulations showed that this particular nose tip 
deformation would cause a radius of dispersion of 0. 1 35 inches at 1 00 yards. 
This is not terribly important in a hunting rifle that likely won’t group better 
than an inch at 100 yards. While I have experienced bullet tip deformation 
of this type and severity in the field, it is unusual to see a bullet deformed 
this badly. So, at least as far as most hunters are concerned this 
error is insignificant. 


Chapter 10 : External Ballistics 

Most bench rest shooters use a match bullet with a small diameter hollow 
point without an exposed lead tip. This type of bullet would be very hard to 
deform as badly as the sample case. Some match hollow point bullets out of 
the box do have a slight angle of the nose flat, that appears to be as much as 
5 degrees. If I scale this estimate of 5 degrees angle, the radius of dispersion 
of a 6mm match bullet would be about 30 to 40 times less than we got on the 
270 SP bullet with a deformed nose. This rough estimate indicates a radius 
of dispersion of 3-5 mils at 1 00 yards for a 68 grain 6mm match bullet. The 
smaller the diameter of the hollow point nose flat the smaller the error. This 
error is essentially insensitive to range, so at long ranges it is completely 

Bullet deformation is the third mode of motion of a projectile and is called 
nutation. This nutation mode rotates at the spin velocity of the bullet. The 
Tricyclic Theory (which means three cycle) includes this nutation mode plus 
the two modes of precession. Nutation was not included in Figures 10-1 
through 10-4 because it would make the graphs confusing. I think you can 
understand the difficulty in experimentally determining the error contributed 
by a deformed bullet tip, because it is so small compared to the normal group 
size. We have already investigated the effect of a canted base in the chapter 
on muzzle blast (Chapter 7). Small irregularities sometimes occur on the 
heel (corner of the base) of bullets. I know no way of evaluating such a small 

Uphill or Downhill 

While the error caused by shooting either up a hill or down a hill is unimpor- 
tant to the target shooter it can be very important to a hunter. The error is 
easily visualized. If you sight in a rifle at some range — say 300 yards so that 
the bullet impact is at the aim point then the sight is adjusted to correct for 
bullet gravity drop. At 300 yards on a high power rifle the gravity drop is 
about 22 inches. Now if you shoot straight up or straight down the gravita- 
tional force will operate along the flight path rather than perpendicular to it. 
This means that the bullet will impact high relative to the aim point by the 
amount of the bullet gravity drop (22 inches) regardless of whether you are 
shooting uphill or downhill. The error can be expressed in equation form as 


Rifle Accuracy Facts 

Up or Downhill Error = GD * Sin(launch angle) 
where GD is the gravity drop in inches at a given range. 

We can come up with a table for specific angles 

Launch Angle(deg) 











Sin(launch angle) 











Error for GD=22 










I think that you can see that if you are shooting either up or down a mountain 
side that has a typical slope of 40 degrees it is easy to shoot over a medium 
sized big game animal. You can get into trouble even at shorter ranges. If the 
rifle is sighted in at 300 yards the midrange trajectory height is about 4.5 
inches above the sight line which adds to the GD at 1 50 yards which is 4 plus 
5 inches (9 inches) at a 70 degree angle. I missed a deer once ( 1 950) that was 
standing on a ledge on a cliff about 150 yards above me. I was shooting 
almost straight up and the bullet went right over his shoulder. Like most 
inexperienced people I had assumed that you should aim high on an uphill 
shot and low on a downhill shot. Not so-you should aim low in both cases. 

Bullet Weight Variability 

Some bench rest shooters weigh their bullets and separate them into various 
weight categories. The question is whether or not all this work is worthwhile. 
I see no way to examine this problem other than to calculate both the internal 
and external ballistics effects of bullet weight variation. Most production bul- 
lets, either hand or machine made, will have a weight variation of about ±0. 1 
grain about the mean weight on a 68 grain bullet (Figure 10-27). The extreme 
spread in weight will be between 0.3 and 0.4 grains. Heavier bullets will have 
a larger variation, but the percentage error will remain about the same. 


Figure 10-27 - Bar chart showing the weight distribution of a box of one hundred 68 
grain match bullets. The extreme spread in weight is 0.35 grains. 

So, I made an internal ballistics calculation to obtain the muzzle velocity on 
a 68 grain and a 68.2 grain bullet to determine the difference in muzzle ve- 
locity. It turned out that the heavier bullet was slower by 2.2 fps. I then 
computed the impact point at 100 yards using the 6DOF trajectory simula- 
tion code with the different weight bullet at the different velocities. The two 
bullets impacted at the same place within 1 mil. In other words, the 0.2 grain 
difference in weight made no practical difference in the impact point of the 
bullet. The reason for this is that there are compensating factors involved. 
For instance, a heavy bullet doesn’t result in as low a muzzle velocity as one 
might think because it causes an increase in pressure over a lighter bullet. 
This is not a simple proportional or linear problem. If you multiply the muzzle 
velocity of the 68 grain bullet by 0.2/68 you would get 8.8 fps if the problem 
was proportional compared to the correct change in velocity of 2.2 fps. Some- 
thing similar happens in the external ballistics. Even though the heavier bul- 
let starts out slower it doesn’t slow down as quickly so that the flight time stays 
very nearly the same. As a result the bullet drop is very nearly the same. 


Rifle Accuracy Facts 

All of this tells me that sorting bullets according to weight is a waste of 
time - except for one thing. And that one thing is the possibility of detecting 
an unbalanced bullet. Sometime ago I was sectioning a bullet when I saw a 
cavity in the lead core. This was a one in a million discovery that is ex- 
tremely unlikely to have happen. This small cavity undoubtedly had a flake 
of some foreign material in it that had been caught and pulled out by the 
milling cutter. It was probably a piece of slag that would have had a lower 
density than pure lead and was large enough to have caused a significant CG 
asymmetry. This bullet was probably lighter than others in the same batch 
and would have probably been detected by weighing. Unfortunately, I didn’t 
weigh this bullet before sectioning it so we don’t know how much the weight 
would have been reduced. By the way, an air bubble of significant size can- 
not exist in a lead core because the extreme pressures used in bullet swaging 
would compress any reasonable size bubble to a microscopic size. However, 
liquids are essentially incompressible and a drop of oil could cause a bubble 
in the core. It is important to realize that lead cores are swaged in a constant 
volume die and the excess lead squirts out of bleed holes. Therefore, the lead 
cores have the same volume as near as it is possible to make them. However, 
the lead wire may not have a constant density, which could explain slight 
variations in bullet weight. Most of the variation in bullet weight (i.e., ex- 
treme spread of 0.35 grains) shown in Figure 10-27 does not come from 
variations in jacket weight and must come from variations in core weight. 
One hundred J-4 6mm match jackets were weighed using an analytical bal- 
ance and found to have an extreme spread of only 0.05 grains. If I were 
going to weigh bullets I would discard the very light ones, because they could 
have cores containing foreign matter and be unbalanced. 

External Ballistics Myths 

There are several ideas floating around in the bench rest community that are 
simply not true. Some of these ideas, which I call myths, are examined. 

1) “Increasing spin rate decreases wind drift”. It was shown that the vertical 
component of wind drift is effected by spin rate but the horizontal 
component is not effected by spin rate. 


Chapter 10: External Ballistics 

2) “A good barrel puts the bullet “to sleep” quickly after muzzle exit and 
therefore the bullet is not effected as much by wind - or those bad 
conditions”. The rate at which the coning motion damps after muzzle 
exit is only effected by the twist rate, bullet inertia characteristics, and 
bullet shape (GS). A so called “good barrel,” whatever that is, has 
nothing to do with the bullet’s performance in bad conditions. 

3) “A bullet goes in and out of stable flight, and if it spends more time in 
stable flight it will be less effected by the conditions and a good barrel 
maintains a higher degree of stable flight”. A typical bench rest bullet 
starts out at around 3200 fps (Mach 2.76) and slows down at the rate of 
roughly 300 fps every 1 00 yards. At 200 yards the bullet will be moving 
at 2600 fps (Mach 2.24). This means that the bullet is supersonic through 
out the first 200 yards of flight and there is no way that the bullet will 
become unstable if it was stable at the muzzle. Furthermore, if a bullet 
becomes unstable enough to be effected differently by the wind it will 
likely completely miss the target. However, at ranges over 600 yards a 
bullet can slow down enough that it enters the transonic range and be 
come unstable. As the angle of attack increases it will slow down rap 
idly and may stabilize again at subsonic velocities. A “good” barrel has 
no significant effect on the bullet’s flight characteristics over a mediocre one. 

4) “Cut rifling produces deeper and sharper rifling marks than button 
rifling and consequently increases the vertical wind drift component”. 
There are several things wrong with this myth. First, the vertical wind 
drift results from gyroscopic effects and has nothing to do with the 
rifling marks. Second, you can make rifling grooves at any depth you 
want with the cut process. I know because I have done it. Third, the 
boundary layer, where the flow is very slow, is thick enough (more than 
3 mils) that the rifling marks are submerged in this layer. Fourth, wind 
tunnel tests show that rifling marks effect the aerodynamic forces by 
only a few percent. 

5) “I have a load that shoots very small groups at 200 yards but doesn’t 
shoot well at 100 yards”. The only way that I can see this happening is 
for the bullet to be launched with a large disturbance at the muzzle. 
While this can happen with magnum rifles with excessive muzzle blast 
pressure, it is very unlikely in the case of a 6BR or a 6PPC bench gun. 
Most likely, this is a case of poor statistics or a change in conditions. 


Rifle Accuracy Facts 


There are several important conclusions to be reached in this chapter. If the 
bullet leaves muzzle at an angle it will immediately start a coning motion 
which causes a corkscrew trajectory. The magnitude of this angular coning 
motion depends on the initial angle and the gyroscopic stability factor (GS). 
For a normal bullet shape the rate at which the coning motion damps with 
range is only dependent on the GS. The radius of the resulting corkscrew 
motion and the resulting dispersion is largely determined by the coning angle 
and the slow precession frequency. It was pointed out that the dispersion 
caused by the corkscrew motion is usually much smaller than the dispersion 
due to the effect of muzzle blast pressure on a canted bullet (Chapter 7). This 
is particularly true for well made bench rest rifles and ammunition. How- 
ever, at very low GS the dispersion due to the coning motion can become 
very large. It was shown how the GS can be determined experimentally with 
a simple test using the vertical and horizontal component of wind drift. We 
also found out that the GS in normal conditions can be reduced by as much as 
20% by a combination of low altitude, high local atmospheric pressure, and 
low temperature. 

The vertical component of wind drift is caused by gyroscopic precession and 
not by Magnus force as some people think. Methods of measuring winds, 
gyroscopic stability, and ballistic coefficient were discussed. The effect of 
nose shape on ballistic coefficient was shown to be significant. The effect of 
variation of bullet weight and shape asymmetries on dispersion were found 
to be small. The effect of muzzle velocity variation and rifle cant was found 
to be significant on bench rest accuracy. 



T his chapter contains comments on problems that didn’t seem to fit in any 
of the other chapters. Also, problems that are not sufficiently supported 
by enough experimental data or theoretical analysis to be considered factual 
are discussed in this chapter. In other words, some of the opinions expressed 
in this chapter are subject to change when factual data become available. 

Bore Fouling and Surface Condition 

A lot has been written about bore fouling, which comes from burned powder 
residue and copper bullet jackets. Most of the bore cleaners either contain 
ammonium hydroxide or ammonium oleate to dissolve the copper fouling. 
Examples of aqueous ammonium hydroxide cleaners are Sweet’s 7.62 and 
Parson’s Household Ammonia. Long before Sweet’s was available I used 
Parson’s Household Ammonia by placing the rifle muzzle down in a coffee 
can with about two inches of ammonia in it. I then alternated pushing a patch 
and a brush on a cleaning rod through the bore. I finished the chore by flush- 
ing the bore with hot water and drying. Well this method would be very 
inconvenient to use at the firing range so I normally did this at home. Sweet’s 
is much more convenient to use and works faster than the household 
ammonia. It also can be used with a patch or brush like any other bore cleaner. 


Rifle Accuracy Facts 

Apparently some barrel makers and gunsmiths have observed bore etching 
with ammonium hydroxide cleaners. Since I had never noticed this problem 
I was puzzled by this. My first thought was that it might be caused by residue 
from the bore cleaner interacting with the powder combustion products at 
high temperatures (6000°F) to form transient reactive molecular species. At 
the time I favored the formation of acids. However, after measuring the pH 
of the residue in the bore after firing and finding it was alkaline (pH=9 to 1 0) 
I was forced to conclude that the mixture deposited on the bore was not acid. 
However, this test does not preclude the formation of transient reactive mo- 
lecular species at high temperatures. By the way, a pH less than 7 indicates 
an acid balance and a pH greater than 7 indicates an alkaline balance with a 
neutral balance occurring at a pH of 7. So, while transient reactive com- 
pounds are probably formed at high temperatures, I concluded that an an- 
swer to this problem required far more complex testing than I could do. I 
believe the bore etching problem might be avoided by swabbing the bore 
with water soaked patches after using aqueous ammonium hydroxide clean- 
ers followed by a cleaner such as Shooters Choice or Hoppe’s. I simply 
clean with Sweet’s every 100 rounds or so and follow that with a patch satu- 
rated in Shooter’s Choice. This works for me. 

Shooter’s Choice and Flitz both contain ammonium oleate, which is the am- 
monium salt of oleic acid. They do remove copper fouling, but they are 
slower than the ammonium hydroxide cleaners. One of my favorite bore 
cleaners is two parts by volume of Shooter’s Choice mixed with one part by 
volume of Kroil. Kroil is a penetrating oil made by Kano Products and I 
believe this idea was suggested by Bill Gebhardt, owner of Bald Eagle Preci- 
sion Machine Company. Liquid Flitz removes copper fouling fairly quickly. 
It is a precious metal polish that seems to polish the bore surface. After using 
Flitz copper fouling seems to be slower in forming. You have to use a brush 
with this stuff and then clean the bore with Shooter’s Choice or some other 
solvent to remove the viscous black gunk that forms. 

Chrome-moly barrel steels may react differently to cleaning chemicals than 
stainless steel barrels. Also barrel steels seem to vary between production 
runs. This makes it even more difficult to evaluate cleaning methods. 

Since everyone has their own idea about how to clean barrels I won’t try to 
tell you how to do it. Instead I will relate to you how some barrel makers and 
gunsmiths recommend that it be done. 


Chapter 11 : Other Problems 

1) Clean every 10 to 20 rounds. 

2) Use a bore guide with inserts at the rear that keeps the rod centered to 
prevent the rod from bowing and rubbing against the rifling. The better 
bore guides have an O ring that prevents cleaning solution from running 
back into the action. 

3) Use uncoated rods because they are much stiffer and less likely to bend 
and abrade the lands. Use a jag tip with patches so that they fall off at 
the muzzle. Pay attention to what you are doing and keep the rod straight 
when pushing the rod through the bore. 

4) Start with 3 patches wet with Shooters Choice-Kroil mixture. 

5) Use a brass brush wet with Shooters Choice-Kroil for about 10 com- 
plete strokes. 

6) Repeat step 4. 

7) Run 2 dry patches through the bore and swab out the chamber with a 
piece of cotton cloth draped on a bore mop. 

The first fouler shot will usually have a velocity 50 to 75 fps lower than 
normal and may not go into the group. 

The Outer’s Foul Out machine may be the only way to get a bore microscopi- 
cally clean but it is very slow. The problem is that bore fouling is laid down 
in alternating layers of combustion products and bullet jacket fouling. As a 
result the Outer’s electronic process stops working when the copper is re- 
moved and there is a layer of carbonaceous powder residue remaining. You 
have to remove the carbon by brushing and then continue the electronic pro- 
cess. However, if you hang in there it will eventually get the bore very clean 
but it may take a few hours. 

There is a form of barrel surface disturbance that has nothing to do with 
cleaning. If you section a barrel that has been fired a lot, the surface will look 
like the surface of an alligator bark juniper or the charred surface of a piece 
of wood (Reference 28). I have seen this in rifle barrels but I am unable 
to make a legible photograph. The photograph in Reference 28 is very good. 
A drawing is shown in Figure 11-1 that shows what this surface cracking 
looks like to the author. This type of surface irregularity is the result of 



Rifle Accuracy Facts 




Figure 11-1 - Artist’s conception of the interior surface of a rifle barrel showing the 
effects of surface thermal cracking. This type of surface imperfection is found in 
barrels that have been fired a large number of times. 

thermal compression stress. When a gun is fired the internal bore surface 
temperatures can reach several hundred degrees and the metal tries to ex- 
pand. Since the internal surface is restrained by the rest of the barrel it can’t 
expand enough and large compression stresses result. These stresses can be 
large enough to cause failure of the steel resulting in a minute surface crack. 
These cracks form in more or less even intervals on the surface resulting in 
the charred wood appearance. Just what effect this thermal cracking has on 
accuracy and how soon it appears, I don’t know. But I doubt that it is a 
good effect. 

About thirty years ago I tried rifling barrels, because I wanted to experiment 
with very slow twists and variable twists, which were commercially unavail- 
able. The rifling in these barrels was very rough, because I was very inexpe- 
rienced. The surprising thing though was that some of these things shot very 
well. I had used the cut rifling method, which consists of pulling a rifling 
head with a single cutter through the bore. The cutter is rotated after each 
pass to give you six grooves, and then the cutter is raised slightly on the next 
set of passes to cut a deeper groove. This method was automated in produc- 
tion so that a rifling machine automatically indexed the rifling head and ad- 
justed the cutter depth of cut. A lot of custom barrels were made back in 
those days using the cut process (I still have one), and they were very smooth. 
Later, practically everyone started using the carbide button swaging process. 
A button shaped with the desired groove and land shape is pulled or pushed 
through a bore that is in between the normal land and groove diameters. It is 
interesting to note that the bore is coated with a light coat of copper before 
the button is pushed or pulled through the hole. It seems that you can’t do it 


Chapter 11: Other Problems 

without the thin copper coating which acts as a lubricant. This is used by all 
the custom barrel makers today that use button rifling, as far as I know. These 
days some of the large commercial barrel makers use the hammer forging 
process. A steel billet with a hole in it is hammer forged onto a rifled man- 
drel. The mandrel is then pulled out of the bore leaving a rifled tube. These 
three methods were discussed in the March 1993 issue of “Guns And Ammo”. 
The factor that drove the change in rifling methods was cost. However, cheaper 
is not always better. The question is, which method is likely to produce a 
better barrel? First of all, I have had no experience with hammer forged 
barrels, and I haven’t seen any data that compares these barrels with the other 
rifling methods. The forged tubes may not have the reamer marks left on the 
lands that appear on both cut and button swaged tubes. However, I don’t 
know about the straightness and thermal drift characteristics of the forged 
barrels. Cut rifling does have sharper corners than button rifling. Whether 
this is good or bad, I don’t know, but I doubt that it makes any difference. 
Both cut and button rifling have variations in groove diameter. You can feel 
the tight spots when you lap a bore. Button rifling may have an advantage 
over cut rifling. The process of swaging work hardens the surface of the 
metal which should reduce wear. Some people think that a slightly tapered 
bore is better, but I don’t think that it has been proved. In any event, I think 
most of this argument over which is best is academic, because unless you 
make your own, you are limited to what you can buy. 

The experts all say that a lapped barrel is better. I have to admit that a new 
barrel that hasn’t been lapped shoots better after it has been fired a few hun- 
dred times. What probably happens is that the bullet picks up enough carbon 
and primer grit, which are abrasives, to lap the bore. If you lap it with abra- 
sive before firing you probably save the throat erosion that occurs during the 
fire lapping process. You can also control the lapping process so that the bore 
diameter tapers to a smaller diameter at the muzzle. However, barrel lapping 
is best done by an experienced barrel maker. 

A new approach to barrel stress relieving has recently appeared (1995) on the 
market. It consists of slowly cooling the barrel to liquid nitrogen tempera- 
tures and then very slowly allowing it to warm up to above room tempera- 
ture. This treatment is supposed to improve stress relief and result in a harder 
steel. Early reports claim reduced bore fouling. However, it is still too early 
to tell whether the improvement is real. 


Rifle Accuracy Facts 

It is hard to say just how bore fouling effects the bullet, but there is one thing 
for sure, and that is that a high pressure magnum will lay down a few tenths 
of a mil of copper in a hundred rounds. This is enough to raise the pressure to 
dangerous levels when a near maximum load is used. So you should watch 
the muzzle of these cannons for copper jacket fouling. Meanwhile, the ex- 
perts are still at odds on the best way to keep a bore clean. 

Case Neck Tension 

The effect of neck tension on the seated bullet has been discussed in various 
magazines. None of these articles that I read seemed to have any real data so 
I decided to try to make some measurements. A load cell was made which 
measures the force required to seat a bullet in the bullet seating die. The load 
cell was an aluminum cylinder with two strain gages on it to measure the 
force. The force was indicated on a milliameter and the peak force required 
to seat the bullet was recorded. The peak force varied between 30 and 70 
pounds. The test was run on a 6mm Remington case with 68 grain match 
bullets. Sixty rounds were tested and segregated into low (<50) and high 
(>50) pounds seating force. The rounds were fired in 5 shot groups through 
an Oheler 35P chronograph in the Tunnel Range with a Heavy Varmint rifle. 
I could tell no difference at all between the high and low seating force in 
average muzzle velocity, extreme spread in velocity, or group size. Conse- 
quently, I am forced to conclude from the results of this limited test that 
bullet seating force has no effect on accuracy. However, this test was run on 
one cartridge and one gun, which is a very limited test and is not necessarily 
conclusive. It may be that a very light seating force (< 1 0 pounds) may result 
in uneven bullet seating depth in the lands. This could result in greater dis- 
persion. However, some successful bench rest shooters use very light neck 
tension and do very well in competition. 

Drift Free Bullet 

Nearly forty years ago I was heavily involved in launching rockets for re- 
search purposes. The first one that we fired turned into the wind as soon as it 
left the launcher and impacted upwind from the intended impact area. 


Chapter 11: Other Problems 

You see the rocket thrust was much greater than the aerodynamic drag which 
causes wind drift and it over corrected. We came up with a computer code 
that allowed us to correct the launch angle to compensate for the wind effect. 
So why not put a small rocket in the base of a bullet that would provide just 
enough thrust to offset the drag force? 

The experience of flying fighter aircraft during WWII that had either 6 or 8 
machine guns (50 caliber) on them supported the idea. You see I noticed that 
while the armour piercing bullets, the incendiary bullets, and the ball ammu- 
nition all impacted in the same place, the tracer bullets impacted higher than 
the others. Since the incendiaries were more visible than the tracers anyhow, 
I had my crew replace all the tracers with incendiaries. This was a more 
effective situation because the tracers were wasted. Well I now know why 
the tracers were so different. It turns out that incendiary bullets have only a 
7% reduction in drag compared to the standard round while a tracer has a 
40% reduction in drag (Reference 27 and 29). This large reduction in aero- 
dynamic drag is caused primarily by the increase in base pressure resulting 
from the burning pyrotechnic mixture in the base of the bullet which pro- 
vides the visible smoke trail. Armed with this information I decided to see if 
it was possible to eliminate wind drift by placing a small rocket in the base of 
a bullet that would offset the aerodynamic drag. 

Well, the first thing to do with an idea like this is to analyze the problem 
theoretically and see if it might work. The 6DOF computer calculations said 
sure enough the wind drift would be eliminated if the drag were zero. The 
next step was to see if you could squeeze a large enough propellant charge in 
the rear end of a bullet. The aerodynamic drag on a 6mm bullet is about 1 
pound. We know the base pressure drag reduction caused by the hot gasses 
in the wake can be as high as 40%. So the rocket thrust may only need to be 
0.6 pounds. 

The better rocket propellants have a specific impulse of about 300 pounds- 
sec of impulse per pound of propellant. We need about 0.6 pounds thrust for 
0.2 seconds (200 yards) and that means we need 2.8 grains of propellant. For 
these conditions we need a cylindrical grain about 0.210 inches in diameter 
and about 0.26 inches long. In Chapter 10 I had tried swaging a plastic cyl- 
inder into the base of a 270 bullet to increase the stability and it worked fine. 
With this in mind I tried swaging a cylinder of model rocket propellant into 



Rifle Accuracy Facts 

the base of a 270 jacket followed by a lead core. A small hole was drilled 
into the base of the jacket before the propellant and lead core were inserted. 
A larger caliber and longer bullet can be made to work at longer ranges, 
probably to 500 yards. 

These prototype bullets were test fired in a strain gage thrust measuring de- 
vice. This is where the trouble started. It was difficult to ignite the rubber 
based model rocket propellant without using a black powder electrical squib. 
When they did ignite with a sufficiently small nozzle hole they occasionally 
would burn erratically. This unsteady burning is known by rocket engineers 
as chugging and sounds like a machine gun. So I decided to test fire some of 
these in a rifle (remotely of course) with a larger than optimum nozzle to see 
if they would ignite in the barrel. They apparently did not ignite in the barrel 
because I could not detect any difference in velocity between inert and live 
rocket rounds at the target. 

Faced with the ignition difficulty I decided to give up on this project for the 
time being because it obviously was going to take a lot more development 
work than I had anticipated. However, I still think it is a practical idea but I 
don’t plan to work on it in the near future. I want to warn the reader to 
take extreme safety precautions if you decide to try this. In some of the 
bench tests the jackets exploded but I was protected by a plexiglass box en- 
closing the experiment plus safety glasses, face shield and padded clothing. 
Unless you have some experience with explosives don’t try it. 

Moly Coated Bullets 

Recently there has been a lot written in the popular literature about coating 
bullets with molybdenum disulfide and carnauba wax. The bullets are first 
coated with molybdenum disulfide (hereafter referred to as moly) and then 
coated with carnauba wax over the moly. The coating is done by tumbling 
the bullets in rotary tumbler filled with steel shot. The idea here is that both 
molybdenum disulfide and carnauba wax are lubricants that should reduce 
barrel friction and improve performance. I decided to try to test the five 
claims that have been made for this process. 


Chapter 11 : Other Problems 

The first claim is that it is possible to achieve higher muzzle velocities at the 
same peak chamber pressure due to reduced barrel friction. They also say 
that at the same powder load a coated bullet will have slightly (3-4%) less 
muzzle velocity due to the reduction in barrel friction. I tested coated and 
uncoated 68 grain 6mm bullets for muzzle velocity and chamber pressure. 
The average muzzle velocity for the uncoated bullets was 3175 compared to 
3083 for the coated bullets. The velocity difference was 92 fps or 2.9% which 
agrees with the claim. The chamber pressure measurements are shown in 
Figure 1 1-2 for the uncoated (top photo) and coated bullets (bottom photo). 
The vertical scale is about 10,000 psi per centimeter. The chamber pressure 
was about 54,000 psi for the uncoated bullets and about 47,000 psi for the 
coated bullets. The effect on chamber pressure and velocity was not changed 
when coated and uncoated bullets were alternated during testing. This 
indicates that there is no residual effect of the coating and it is just being 
blown out the barrel. The drop in pressure and velocity is not caused by a 
reduction in barrel friction as proposed by Norma and others. It is caused by 
the hot propellant gasses (5640°F) vaporizing the coating resulting in a cool- 
ing (about 400°F) of the propellant gasses. The reason that I am certain 
about this is that if you use a sophisticated internal ballistics code and greatly 
reduce the barrel friction the pressure drops slightly and the velocity increases 
slightly. It is physically impossible to get the measured effect on pressure 
and velocity by reducing barrel friction. Barrel friction has only a small 
effect on velocity. On the other hand, vaporization of a lubricant takes a lot 
of energy and a 400°F temperature drop is very likely. Molybdenum disul- 
fide begins to sublime at 842°F and melts at 4802°F. In order to prove this 
idea I decided to run a test where I simply placed 0.07 grains of moly and 
0.07 grains of carnauba wax in the top of the case on the powder. I had found 
that the difference in weight between the coated and uncoated bullets to be 
about 0. 1 5 grains. The measured chamber pressure was reduced by about 
4500 psi and the average velocity was reduced by 50 fps. This result is simi- 
lar to the pressure - velocity results that I got when testing the coated and 
uncoated bullets although the effect was a little less. One could probably 
fool around with the ratio of moly to wax and achieve identical results to the 
coated - uncoated bullet test. Anyhow, this test convinced me that molybde- 
num disulfide cools down the propellant gasses and reduces the pressure. In 
any event, the loss in chamber pressure has nothing to do with bullet friction. 
The final step was to increase the load in the 6BR from 27 to 28 grains of 


Rifle Accuracy Facts 

N133 and try to drive the coated bullets at the same pressure level and mea- 
sure the velocity. The pressure curve was almost identical to the uncoated 
bullet pressure data shown in the top photo in Figure 1 1-2 and the velocity 
was 13 fps higher. Norma claims up to 10 meters/sec (32.3 fps) increase in 
velocity at the same peak pressure, which is possible. Anyway, I didn’t find 
the increase in velocity performance very encouraging. 






r 0 0 0 B 


,000 1 


,000 1 






Figure 11-2- Oscilloscope traces showing chamber pressure measurement with 
and without molybdenum dissulfide and carnuba wax coating. The top photo shows 
a peak chamber pressure of about 54,000 psi (muzzle velocity of 3175 fps) for the 
uncoated bullets and the bottom photo shows a peak chamber pressure of about 
47,000 psi (muzzle velocity of 3083 fps) for the coated bullets. N133 powder and 68 
grain 6mm match bullets were used. 


Chapter 11: Other Problems 

There have been claims that the coated bullets impact higher on a target at 
long range (600 yards) implying an increased ballistic coefficient and flatter 
trajectory. I measured the velocity loss over 1 00 yards on uncoated and coated 
bullets. The uncoated bullets lost 325 fps and the coated bullets lost 323 fps 
over the 100 yards range. The difference of 2 fps is within the limits of 
measurement accuracy, so I am forced to conclude that there is no difference 
in ballistic coefficient. Further, there is no reason to expect to see a signifi- 
cant difference in BC because the coating will be gone shortly after the bullet 
leaves the muzzle if not before muzzle exit. The bullet is hot (600°F) and the 
aerodynamic boundary layer is hot (750°F), so the wax coating will vanish 
almost instantly if any is left after going through the barrel. Also, there is no 
basis for the idea that any lubricant coating can reduce aerodynamic skin 
friction drag. If it did reduce aerodynamic drag, it could only be a small 
effect because skin friction drag is only a small part of the total drag on a 
bullet. Also, the idea that the lubricant somehow reduces the coning angle of 
attack enough to reduce the aerodynamic drag and increase the ballistic coef- 
ficient is not reasonable. This was shown in Chapters 7 and 10 
(Figure 10-20). I would think that reports on bullets striking higher on a 
distant target are due to optimistically increasing the muzzle velocity and 
chamber pressure or due to firing at a different point on the high frequency 
barrel vibration curve (Chapter 4). 

There are claims of improved accuracy of up to 20%. I did not find this to be 
the case with my rail gun which averages 0. 175 inches at 100 yards. With the 
same optimum load of 27 grains of H322 and the same lot of bullets coated I 
got an average group size of 0. 179 compared to 0. 175 inches for the uncoated 
bullets (see Figure 4-40). Of course, the muzzle velocity was 92 fps less than 
it was with uncoated bullets at the same load. When I tried the higher load of 
28 grains to obtain the same muzzle velocity as the uncoated bullets, the 
group size increased to about 0.3 inches. As far as I could see the accuracy 
was not improved, but this is one gun under one condition. The results could 
be different with different cartridges or guns. Also I made no attempt to 
optimize the situation. One thing that did occur to me was that if you don’t 
get a good, even coating of this stuff on the bullet you could make the CG 
offset worse. Molybdenum disulfide has a density that is about 40% that of 
lead. So, an uneven coating could make a difference. I believe that I had as 
good a coating as I could get. 

Rifle Accuracy Facts 

It has been claimed that moly coated bullets have reduced fouling charac- 
teristics. I believe this could be true, although I didn’t fire enough coated 
bullets to allow a quantitative estimate of the effect. However, I had the 
impression that you don’t have to clean the bore as often. 

Norma claims that barrel life is extended with the coated bullets. I think this 
may be logical and may be true. After all the pressure and temperature are 
reduced for the same load which should reduce barrel erosion. However, I 
don’t want to fire tens of thousands of rounds through several barrels to find 
out. So you can be the judge of that claim. 

In summary, I could find no evidence of significantly improved velocity- 
pressure performance, accuracy, or ballistic coefficient. The coated bullets 
seemed to require less bore cleaning. The effect on barrel life was not tested. 
In this limited test I could see no reason for using coated bullets 
for my purposes. However, you may want to try it because you may get 
different results. 

Shooting Technique 

While I don’t claim to be a great shot with a rifle, I have made a few observa- 
tions over a period of 60 years of shooting all kinds of rifles that may 
be of interest. 

I am convinced that the biggest problem in shooting well in hunting big game 
is getting excited (“buck fever”). By the time I had gotten around to hunting 
trophy big game I had pretty much gotten over getting excited. I think it just 
takes experience and it helps to start out hunting varmints. It also helps to get 
out and shoot at rocks or stumps at unknown ranges. After you shoot at a 
target of opportunity, pace off the distance. It’s easy to get fooled as to the 
range, particularly in mountainous terrain, and this practice helps. If you can 
regularly hit a “stump deer” you can probably hit a live deer. Another thing 
that gets people into trouble is heavy breathing and a pounding pulse. It 
helps to stop in your tracks and let your breathing and pulse rate slow down. 
You need to stop and look around often anyhow. I usually move slowly and 
stop every 50 to 100 feet for as much as a minute. That way you are never 
winded. This is particularly important for people who live at low altitude and 
try to hunt at high altitude (say 9000 feet). Another thing that is important 


Chapter 11: Other Problems 

is to always try to shoot from a sitting position. Most people practice 
shooting off a bench at a rifle range. Try to practice shooting in rough coun- 
try from a sitting position. I don’t try to get any closer than 200 yards. That 
way the animal is undisturbed and I have plenty of time to get into a sitting 
position and relax. Try it — you’ll like it! By the way, don’t sight in your 
hunting rifle by shooting it off a hard sandbag rest. If you do, it very likely 
will have a different point of impact when you shoot from either an offhand 
or sitting position. Use something like a rolled up sleeping bag under the 
forearm. Never use slings wrapped around your arm in the army style be- 
cause they also affect the point of impact. 

Bench rest match shooting is something else and I haven’t had a lot of expe- 
rience at it. There are two main ways to shoot — the firm hold and the free 
recoil method. While there are variations in the firm hold technique, you 
usually grasp the pistol grip and hold the butt firmly against the shoulder. We 
have found that small differences in the firmness of the hold can cause differ- 
ences in the vertical impact point. Consequently, if you use this approach in 
match shooting you must be very careful to use a uniform hold while shoot- 
ing a group. With the free recoil method you aim the rifle by adjusting the 
front rest and only touch the trigger to fire it. Therefore, you eliminate the 
problem of holding uniformly and also you can watch all the wind flags con- 
stantly. The disadvantage is that the free recoil method is slower than the 
firm hold method. The only thing to do is to try both methods and see which 
one works best for you. 

One thing that may be a problem is the hard sandbags used in bench rest 
shooting. I know for certain that guns with heavy recoil don’t shoot well off 
a standard bench rest setup. Just where this starts being a contributor to 
dispersion is difficult to say but I am suspicious of these hard bags even in the 
case of 6mm bench guns. Unfortunately the bench rest rules specify the use 
of sandbags. 

Statistical Error 

I often see magazine articles where someone makes extravagant claims and 
presents as few as two 3-shot groups as experimental proof. Well, this is not 
enough data to prove anything. A series of 3-shot groups will average about 


Rifle Accuracy Facts 

half to two thirds the dispersion of a a series of 5-shot groups. Also, it takes 
at least five 5-shot groups to begin to have any confidence in the data. The 
average group size data reported in this book are based on a minimum of 
eight 5-shot groups. However, it usually is not necessary to fire more than 
ten 5-shot groups to have reliable data. 

A Final Word 

I have tried to present facts about rifle accuracy as much as possible. Obvi- 
ously, there are still problems that remain to be solved but I believe we know 
a lot more about rifle accuracy than we did when I started this research. I am 
still working on some of the unsolved problems and may eventually write a 
second volume. The computer programs used in this work will not be avail- 
able to the general reader because they are not user friendly and I don’t have 
time to thoroughly document them. Also, I do not build guns for people. I 
hope Remington is not offended by some of my analyses of the Remington 
721 rifle. As a matter of fact, the Remington 700 rifle is my favorite sporter 
and I have several. My objective was simply to improve it. Anyhow, I hope 
you have found this interesting reading. Good Shooting! 


The reader is warned one last time that some of the experiments performed 
for the book can be dangerous and should not be duplicated by people 
who do not have an extensive background in test techniques and in explo- 
sive technology. 




E arly in this work it was discovered that, although a sporter barrel vi- 
brates in many modes, the most important was the third mode at a fre- 
quency of about 1.25 kHz. The higher modes simply don’t contribute much 
to dispersion, because even though relatively large accelerations are present 
at these high frequencies, the displacement caused by these modes is very 
small. Therefore, the task was to design an accelerometer that would pre- 
dominantly respond faithfully to this third mode. There are several types of 
accelerometer designs that are commonly used. Three types were tried in 
this investigation. 

1 ) piezoelectric crystal - Many commercial accelerometers are of the pi- 
ezoelectric crystal type. They are sensitive, having a high electrical out- 
put, and respond well over a large frequency range. However, they are 
sensitive to shock in all directions, and tend to vibrate at their natural 
frequency, which can be 30 kc and higher. I made several of these, using 
a Radio Shack crystal microphone, and it worked very well at low accel- 
erations when tested on the bench where there is little or no shock exci- 
tation. However, when tested on the muzzle of the rifle, where there are 
a lot of shock waves running through the barrel, the data were obscured 
by a lot of high frequency oscillation. In fact, it appeared that the instru- 
ment was driven into saturation at the high frequencies. When the out- 
put was run through a low pass electronic filter, the lower frequency data 


Rifle Accuracy Facts 

that is of interest began to appear. However, when the output of the 
accelerometer is partially saturated, the low frequency data are likely to 
be badly distorted. Attempts to damp the accelerometer, in an effort to 
attenuate the motion of the sensing crystal, were completely unsuccess- 
ful. Perhaps one could do better with a commercial accelerometer of 
this type, but I believe one would have a similar problem. My experi- 
ence with the piezoelectric crystal type led me to discard this approach 
and try the beam type of accelerometer. 

2) strain gaged beam - The strain gaged cantilever beam has been used 
extensively in the past. It has the advantage of being easy to damp and is 
very predictable. It has the disadvantages of low electrical output, and 
has to have a low natural frequency. As a consequence of the low electri- 
cal output, it has a poor signal to noise ratio. The low natural frequency 
is not a problem in this application. However, the low sensitivity of a 
strain gage bridge, requires high levels of amplification (i.e. 2000), and 
this leads to noise problems. Since the sensitivity of the strain gage 
bridge is directly related to the natural frequency of the beam, the de- 
signer is caught between two conflicting requirements, if the natural fre- 
quency is to be greater than a few hundred Hertz. This application re- 
quires a natural or resonant frequency of around 2 kHz, which automati- 
cally means that the sensitivity will be low. Even though an extensive 
effort was made to solve the noise problem, including an imbedded am- 
plifier chip in the accelerometer carrier near the beam, I realized that 
low level accelerations (i.e. < 10 G’s) would be obscured. Consequently 
another approach to the beam type of accelerometer was taken. 

3) piezo film coated beam - Piezo film is a thin polyvinylidene flouride 
plastic film, that develops large voltages when stretched or compressed. 
The thickest film, which was 4.2 mils (100 micrometers), was used. The 
film is called Kynar, and is produced by Pennwalt Corporation (phone 
215-337-6710). Both sides of the film are coated with a metallic coat- 
ing, which provides an electrical connection. While electrical contact 
can be made with a silver loaded epoxy, I found that mechanical contact 
was satisfactory and somewhat easier to do. While it is not as sensitive 
as piezo crystal materials, it is far more sensitive than a strain gage. For 
this application an op-amp amplifier with a gain of 50 resulted in an 
output of several volts at an acceleration of 25 G’s. The amplifier is 
embedded in a small cavity (.35x.75x.2 inches) in the body of the 


Appendix- A: Accelerometer Design 

accelerometer carrier. The signal to noise ratio was very high even at 
low acceleration levels, because the noise level was only a few milli- 
volts. The output of the piezo film must be fed to the amplifier through 
a field effect transistor for proper impedance matching. Piezo film has 
one undesirable characteristic, and that is the electrical-mechanical cou- 
pling (i.e. voltage output for a given deformation) changes with frequency. 
The electrical coupling changes by a factor of two between 50 Hz and 
about 150 Hz. This frequency range was avoided in this application. 
Above 150 Hz the coupling is constant. 

Accelerometer Design 

The accelerometer is deliberately designed to exclude vibration above about 
2 kHz. To accomplish this filtering, the beam was designed to have an un- 
damped resonant first mode frequency of 3 kHz without the film. The di- 
mensions of the beam made of steel shim stock are 0.015 inches thick by 0.2 
inches wide and 0.40 inches in length. When the film is bonded to both 
surfaces of the beam and 0.55 of critical damping added, the resonant fre- 
quency was lowered to 2 kHz. A photograph of the complete accelerometer 
mounted on the muzzle of the rifle was previously shown in Figure 4-21. 
A cross-section drawing of the accelerometer beam is shown in Figure A-l. 

Figure A-1 - Cross-section drawing of the muzzle accelerometer. 


Rifle Accuracy Facts 

The film is bonded to the free end of the beam with epoxy. The electrical 
contact shown in the figure, plus a connection to the body of the accelerom- 
eter provide the circuit connections. The cavity in the top of the accelerom- 
eter, that contains the beam, is about 0.35 inches wide, and is filled with 
silicon oil through a threaded hole in the cover that is not shown. The cover 
is sealed with Locktight. The silicon oil has a viscosity of 25000 centistokes 
and is made by Dow Corning. The oil has a consistency about like that of 
honey, and has to be inserted with a small tube. All of the air must be re- 
moved by allowing the device to sit for several hours. The oil provides a 
damping factor of between 0.5 and 0.6. Any damping fluid that is used must 
have a very high electrical resistance to prevent charge leakage from the piezo 
film. The accelerometer is only useful in making dynamic measurements, 
because the charge on the film will decay in a static environment. 

The calculated amplitude ratio and phase characteristics for the accelerom- 
eter beam are shown in Figure A-2. Note that the amplitude ratio is flat to 
within 10% out to about 2 kHz where it starts to roll off, so that the higher 
frequencies will be attenuated. While the amplitude characteristics are just 
what are desired, a 40 degree phase lag results at the frequency of most inter- 
est (1.25 kHz), and that is not a desirable feature. Fortunately, this can be 
corrected by designing a band pass filter that will have a similar sized phase 
lead at 1 .25 kHz. Also, the bandpass filter will further attenuate the higher 
frequencies, which is the main purpose of the filter. 

Figure A-2 - Graph showing the frequency response characteristics of 
the accelerometer. 


Appendix- A: Accelerometer Design 

Bandpass Filter 

A bandpass filter was used instead of a low-pass filter, because of its phase 
lead characteristic at frequencies below the center frequency. The filter is 
designed to have a phase lead as near 40 degrees at 1 .25 kHz as possible, 
which means that the center frequency has to be somewhat higher than the 
first mode frequency. The amplitude ratio and phase characteristics are shown 
in Figure A-3 for the filter that was used. It has a center frequency of 1 .4 kHz 
and a gain of two. The filter was designed to have a Q of two and a band- 
width of 700 Hz. The phase lead is about 35 degrees at the first mode fre- 
quency ( 1 .25 kHz), which comes close to compensating for the 40 degree 
phase lag induced by the accelerometer beam. These calculated response 
characteristics were confirmed by experimental bench tests. The filter was 
designed using the equations provided by Berlin in Reference 30. The cir- 
cuit for the bandpass filter is shown in Figure A-4. Now, the response char- 
acteristics shown in Figure A-3 are for steady state conditions, and the input 
to the filter is not steady state in this application. The only thing to do is to 
use the differential equation that expresses the behavior of the filter and sub- 
ject this equation to an artificial, but representative input from the barrel vi- 
bration code. In this way a calibration factor can be obtained as the ratio of 

Figure A-3 - Graph showing the frequency characteristics of the bandpass filter 
used to filter out unwanted signals. 


Rifle Accuracy Facts 

Figure A-4 - Circuit of the bandpass filter. 

the input to the output voltage for the typical first mode oscillation of the 
barrel. The calibration factor turned out to be 0.52 compared to the steady 
state value of 0.82 at a frequency of 1 .25 kHz. The filter doesn’t have time to 
reach an equilibrium steady state condition. Since the second order differen- 
tial equation used for the transient response calculations seems to be difficult 
to find in the literature, it is shown below for the benefit of professional 

(d 2 /dt 2 )Eo = -2/(R3*C)*(d/dt)Eo - (Rl+R2)/(Rl*R2*R3*C 2 )*Eo -1/ 

where Eo is the output voltage, Ei is the input voltage, and the asterisk (*) 
indicates multiplication. 

Figure A-5 - Circuit diagram of the integrator used to obtain the muzzle vertical 
velocity and vertical deflection. 

The circuit used for the integrators, which provide lateral muzzle velocity 
and displacement from the acceleration output of the bandpass filter, is shown 
in Figure A-5. The output of the bandpass fdter is fed to the input of the first 
integrator, which has an output proportional to velocity, and the output of the 
velocity integrator is fed to the input of the second integrator, which has an 
output proportional to the deflection of the muzzle. The gain of the circuit is 
10000, which results in a calibration of 0.427 inches/sec/volt for velocity, 
and 0.043 mil/volt for deflection. Note that screw adjustable potentiometers 
are used for all resistors, which facilitates exact adjustment. All three variables, 
acceleration, velocity, and deflection can be compared with the computed 
variables obtained from the barrel vibration computer code. In addition, 
integration has a low-pass filtering effect, which makes the experimental 
velocity and deflection easier to compare and analyze. Also, lateral velocity 
and deflection are the two parameters that cause bullet dispersion. 



Rifle Accuracy Facts 


Calibration of the device begins with vibrating the accelerometer, without 
the bandpass filter, on the end of a 3/4 inch diameter rod mounted in a lathe. 
The cross feed of the lathe is used to deflect the end of the rod a known 
amount, and the carriage feed is used to release the rod so that it vibrates 
freely. The length of the rod can be varied to change the frequency, however 
the frequency was generally in the range of 30 to 50 Hz for these tests. The 
acceleration at the end of the rod can be calculated from 

A = d*(f/(2*7t) ) 1 2 /G 

where f is the frequency in Hz, G is the acceleration of gravity (32. 1 6 ft/sec 2 ), 
d is the lateral deflection in feet, and A is the lateral acceleration in G’s. The 
deflection used was enough to produce 20 to 30 G’s. The output voltage is 
recorded on the oscilloscope for analysis. The results indicated that the sen- 
sitivity of the accelerometer is 0.087 volts/G at low frequencies, and is twice 
that, or 0.174 volts/G at frequencies above about 100 Hz. Recall that the 
manufacturer provides data showing that the piezo film is twice as sensitive 
at high frequencies. Of course, it would be better to calibrate the accelerom- 
eter at a higher frequency (say 1 kHz), however this requires a professional 
piece of equipment which was not available, and not sensible for me to try to 
construct on an amateur basis. The acceleration data from the vibrating rod 
was also used to check the performance of the barrel vibration code and the 
agreement was excellent. The accelerometer data on the actual barrel (held 
in the lathe) was used to obtain a viscous damping coefficient for use in the 
barrel vibration computer code, by determining the number of cycles required 
to damp to half amplitude. The damping factor was 0.03, which is typical of 
mechanical vibration systems. 

The total accuracy of the acceleration instrumentation is probably no better 
than 10%. There are several reasons for this relatively low accuracy. 

1) The calibration had to be performed at a much lower frequency than the 
frequency of interest, because of equipment limitations. Consequently, 

the calibration depends on the frequency dependence data supplied by 
the manufacturer. 


Appendix- A: Accelerometer Design 

2) The reading accuracy on the oscilloscope record is probably no better 
than a few percent. 

3) Cross axis sensitivity is the biggest contributer to inaccuracy in the cali- 
bration, even though it is undoubtedly much reduced by allowing the 
accelerometer to slide in the axial direction during the time of measure- 
ment. Since the friction force in the axial direction is roughly 1 .5 pounds 
and the accelerometer weighs about 0.16 pounds the axial acceleration 
acting on the accelerometer should be roughly 10 G’s. The cross axis 
sensitivity was measured and found to be between 5% and 7%. There- 
fore, the error should be roughly 0.5 to 0.7 G’s, which is a relatively 
small percentage of the peak accelerations (30 G’s) that were observed. 
Since there isn’t any way to evaluate this error directly, there isn’t any 
way to be absolutely sure of the error in the actual case. 

4) The transient response of the bandpass filter is another source of uncer- 
tainty. The transient response of the filter depends on the characteristics 
of the input, and while the actual input was simulated there is still some 
uncertainty. The only other thing that might be done is to differentiate 
the experimental output of the filter (i.e. inverse transform), using the 
differential equation for the filter, to try to obtain the actual transient 
response of the filter. This is a difficult undertaking, and was not done. 

5) Temperature and other miscellaneous effects were not evaluated. 

In spite of the fact that the instrumentation accuracy is not as good as the 
author would like, it is probably accurate enough to serve the purposes for 
which it was intended. In fact, 20% accuracy would have been good enough 
to determine how the muzzle vibrates, and to determine whether or not the 
corrections made to the rifle were effective in reducing vibration. I believe 
that the accelerometer instrumentation has been successful in these respects. 

Rifle Accuracy Facts 






T his appendix is necessarily written at a higher technical level than the 
rest of the book, and requires an engineering background for thorough 
understanding. In spite of this necessary complication, the average reader 
may wish to scan it for a better understanding of how the barrel vibration 
code works, and to gain a better comprehension of the complexity and depth 
of the work. 

Several approaches were taken in developing the computer code to simulate 
barrel vibration. The coupled multiple body approach proved to be the most 
practical for use on a small personal computer. The barrel is divided into 25 
elements or bodies, which is schematically shown in Figure 4-27. The taper 
in the barrel is much more gradual than that indicated by the computer graph, 
because of the limited number of CRT pixels. Each element is treated as a 
constant diameter cylinder. It was found that at least 25 elements per wave- 
length of the highest mode of oscillation were required. In this case the third 
mode, which is the one of interest, represents approximately one wave length 
over the length of the barrel (see Figure 4-28). Attempts to run this code for 
larger numbers of elements, in order to obtain modes higher than the third, 
proved fruitless and were abandoned because the computing times were ex- 
cessive. The author’s computer is a Gateway 2000 with an Intel 486 proces- 
sor running at 66 megacycles. Computing time for a typical case under these 
conditions is about 6 minutes. The computing time is roughly proportional 


Rifle Accuracy Facts 

to the cube of the number of elements, because the time step has to be re- 
duced as the number of elements is increased. Consequently, a main frame 
computer is required for calculations involving substantially greater num- 
bers of elements. The code simulates vibration in the lateral direction, which 
is perpendicular to the bore axis, resulting in a single degree of freedom code. 
Calculations were primarily done in the vertical plane. The single degree of 
freedom approach should be valid for this application where the deflections 
are small and rotation of the elements is very small. In applications involv- 
ing large deflections, it may be necessary to include the effects of rotation. 
In applications to thick beams, it may be necessary to include the effects of 
shear deformation, however the barrel is a long slender beam, and the shear 
effects are not included. The differential equations that describe the motion 
of each element are 

A[i,j]*M(J]*d 2 Y[j]/dt 2 + Y[i] + C[i,j]*dY[i]/dt = A[i,j]*F[j] 

where A[i,j] is the influence coefficient for the i’th element with a driving 
force F[j] at the j’th element, M[j] is the mass of the j’th element, Y[i] is the 
deflection of the i’th element, C[i,j] is the damping coefficient, dY[i]/dt is 
the velocity of the i’th element, and d 2 Y[i,j]/dt 2 is the acceleration acting on 
the i’th element with a force applied on the j’th element. The equation must 
be solved for the acceleration, which provides 

d 2 Y[i]/dt 2 = (-Y[i]-Z(inertial)+A[i,j]*F[j] )/(A[i,i]*M[i]) 



E(inertial) = E{A[i,j]*M[j]*(d 2 Y[i,j]/dt 2 )} 

-A[i,i]*M[i]*(d 2 Y[i]/dt 2 ) 


Appendix-B: Barrel Vibration Computer Code 

The sum of the inertial terms is the sum of the effective forces acting on the 
i’th element as a result of inertial forces acting on all the other elements. In 
order to clarify this, we write the equation for the first element, where a 
single driving force is located at element 1. 

d 2 Y[l]/dt 2 = { -Y[ 1 1 + F[l]/M[l] -A[l,2]*M[2]*(d 2 Y[2]/dt 2 ) 
-A[l,3]*M[3]*(d 2 Y[3]/dt 2 ) -A[l,4]*M[4]*(d 2 Y[4]/dt 2 ) 

-A[ 1 ,5]*M[5]*(d 2 Y[5]/dt 2 ) -A[ 1 ,6] *M[6]*(d 2 Y[6]/dt 2 ) 

- A[ 1 ,7] *M 1 7] *(d 2 Y [7]/dt 2 ) -A[l,8]*M[8]*(d 2 Y[8]/dt 2 ) 

-A[ 1 ,9]*M[9]*(d 2 Y[9]/dt 2 ) -A[l,10]*M[10]*(d 2 Y[10]/dt 2 ) 

-A[ l,ll]*M[ll]*(d 2 Y[ll]/dt 2 ) -A[l,12]*M[12]*(d 2 Y[12]/dt 2 ) 

- A [ 1 , 1 3] *M[ 1 3]*(d 2 Y[ 1 3]/dt 2 ) -A[ 1 , 1 4] *M[ 1 4] *(d 2 Y[ 14]/dt 2 ) 
-A[l,15]*M[15]*(d 2 Y[15]/dt 2 ) -A[l,16]*M[16]*(d 2 Y[16]/dt 2 ) 

-A[ 1 , 1 7] *M[ 1 7]*(d 2 Y[ 1 7]/dt 2 ) -A[ 1 , 1 8] *M[ 1 8]*(d 2 Y[ 1 8]/dt 2 ) 

-A[ 1 ,19]*M[ 1 9]*(d 2 Y[ 1 9]/dt 2 ) -A[ l,20]*M[20]*(d 2 Y[20]/dt 2 ) 
-A[1,21]*M[2 1 ]*(d 2 Y[2 1 ]/dt 2 ) -A[ 1 ,22] *M[22]*(d 2 Y[22]/dt 2 ) 

-A[ 1 ,23]*M[23]*(d 2 Y[23]/dt 2 ) -A[l,24]*M[24]*(d 2 Y[24]/dt 2 ) 

-A[ 1 ,25]*M[25]*(d 2 Y[25]/dt 2 )}/(A[ 1 , 1 ]*M[ 1 ] 

-C [ 1 ] * (d Y [ 1 ]/dt)/M [ 1 ] 

So, we have to solve 25 of these equations simultaneously for the accelera- 
tion on each of the 25 elements. This is done on a computer by simply put- 
ting the following equation in a loop that sums the terms over j for each i. 

I(inertial) = I{ A[i,j]*M|j]*d 2 Y|j]} 

-A[i,i]*M[i]*(d 2 Y[i]/dt 2 ), j=l to 25 for all i’s 

Then one subtracts A[i,i]*M[i]*d 2 Y[i]/dt 2 from the sum of the acceleration 
forces and plugs the result into 

d 2 Y[i]/dt 2 ={-Y[i]-Z(inertial)+A[i,j]*F[j] }/(A[i,i]*M[i]) -C(i,j)*dY/dt/M[i] 

This equation is solved for each i element. It should be noted that I found 
that the solution was greatly stabilized by multiplying the summation of ac- 
celeration term by a factor slightly less than one (i.e. 0.99 to 0.995). The 
reason for this is unknown, but may be due to the limited 32 bit word length 
of the small computer. A fourth order Runge-Kutta integrator is used to inte- 
grate the accelerations to obtain velocities and then the velocities are inte- 
grated to obtain displacement. The new values for acceleration, velocity, and 


Rifle Accuracy Facts 

displacement are substituted back into the equations and the equations are 
solved again for new values of the variables (i.e. state variables). This pro- 
cess is repeated until the accelerations stop changing significantly, at which 
time the solution has converged. At this point the solution continues to the 
next time step. The number of iterations was arbitrarily limited to 50 after 
some experience was gained in operating the code. The time interval for 
each step was chosen to be one microsecond. This is adequate for the fre- 
quency of the stiffest element (i.e. element 1) at the fixed end of the barrel. 
Matrix solution schemes were not tried, because the solution used was satis- 
factory. Successive Over Relaxation (SOR) was used to speed up the conver- 
gence. A SOR convergence factor of 1 .2 seems to be optimum. The constant 
convergence criteria used was usually in the region of 0.06 G, however this 
depended on the individual problem. A better convergence criteria might be 
to have a variable criteria applied that depends on the stiffness of the 
individual elements. The boundary conditions are simply zero for all 
state variables. 

In the general case one can have applied forces at all elements, however in 
this specific case the recoil and other receiver moments are applied at ele- 
ment 1. In solving for the gravity droop a constant one G acceleration is 
applied at all elements, and the solution is allowed to continue until the bar- 
rel stops moving. The deflection at each element due to gravity is saved in an 
initial condition file for starting the code for the usual vibration solution. 
The gravity droop has little effect on dispersion. It can have an effect on the 
point of impact for different elevation angles of the rifle. As the rifle is el- 
evated from the horizontal, the gravity droop reduces, causing the bullet to 
strike higher on the target. Other special conditions were investigated, such 
as the centrifugal force caused by the bullet traveling along the curved path 
due to gravity droop, the effect of centrifugal force developed by a spinning 
unbalanced bullet, barrel stiffening due to pressurization, and others. None 
of these effects appeared significant, and are not shown in the equations in 
order to avoid excessive complication. 

The influence coefficients (i.e. A[i,j]), provide the coupling terms between 
the elements. They are the static deflection caused at the i’th element by a 
unit (1 pound) force applied at the j’th element, and in effect are the recipro- 

Appendix-B: Barrel Vibration Computer Code 

cal of the usual spring constant. They are solved for by simply solving the 
static deflection equations, which are 

for i>j 

dY[i,j] = dx*dx 2 /(6*EI[i]*(3*(j-l)+2) 

dY[i,j]/dx = dY[i-l,j]/dx + dx 2 /(2*EI[i]*(2*(j-l)+l)) 

Y[i,j] = Y[i-l,j] + dx*dY[i-l,j]/dx +dY[i,j] 

A[i,j] = Y[i,j J/l 2 

for i>j 

dY[i,j]/dx = dY[i-l,j] 

Y[i,j] = Y[i-l,j] + dx*dY[i,j]/dx 
A[i,j] = Y[i,j]/12 

where x is the distance along the barrel from the fixed end, E is Young’s 
Modulus (30 million psi), I is the moment of inertia of the cross-section, dx 
is the length of the element ( 1 inch), Y is the vertical deflection, and A is the 
needed influence coefficient. Since Y will be in inches with the usual units 
for I and E, Y is divided by 12 to obtain A in feet/pound. The reader should 
note that a force, including inertial forces, acting at any element influences 
the motion of all other elements. This is what couples the bodies together. 

The stiffness of the first element, which is the forward receiver ring, was 
determined experimentally by using strain gages on the ring. It was found 
that the stiffness (i.e. E*I) was about 70% of the calculated value. This is not 
surprising, because the ring is a complicated structure making calculations 
difficult. Also, no cantilever beam ever has complete end fixity, and this one 
is no exception. In calculating the influence coefficients, the mass is as- 
sumed equally distributed along the length of the element. 

In addition to the main part of the code, the moments resulting from bolt and 
recoil force are computed from a table of chamber pressures obtained from 
experimental measurements. The recoil moment was obtained from a two 
body spring mass model, where the first body consists of the barrel, action, 
and scope, which is connected by a spring to the second body consisting of 
the stock. The stock spring constant was determined to be in the region of 
100,000 pounds/inch with analytical methods. A value of 96,000 pounds/ 

Rifle Accuracy Facts 

inch proved to give good results in the code. This spring constant represents 
the compression of the wood stock behind the recoil lug as the recoil force is 
applied to the stock. It has the effect of delaying the onset of the applied 
moment to the receiver. These applied moments are then input as a force 
acting at the end of element 1 with a moment arm of one inch. The response 
moment can be determined from the deflection at the first element using the 
beam equation. The response moment is, of course, the moment that is mea- 
sured by the strain gages, and is less than the applied moment. The longitu- 
dinal position of the bullet was also input in table form from the data in 
Chapter 2. There is also graphic coding required to plot the barrel and its 
deflection. Since graphic coding is sensitive to the particular computer in- 
volved, it is not presented. 

The code was successfully checked by comparing with muzzle acceleration 
obtained from bench vibration tests on both a 3/4 inch constant diameter rod 
and the actual barrel. These tests were described in Appendix A. 

Several hundred computational runs were made with this code over a period 
of two years for the purpose of studying the effect of various inputs on barrel 
vibration. It was invaluable in researching the causes of barrel vibration and 
finding out just how the barrel moves, and how much dispersion is caused by 
the movement. The barrel vibration code has not been documented, and is 
not user friendly, although it could be. Consequently, it is not available to the 
public at the present time. 




A dynamic balance device is preferable to a static balance device, be 
cause it not only measures the CG lateral displacement (i.e. offset), 
but can be used to measure the principal axis tilt with respect to the geometri- 
cal axis. The principal axis is the axis about which a projectile will spin in 
free flight. The dynamic balance device is usually more dependable and 
sensitive than a static balance device. However, the static balance device is 
easier to make and requires less equipment to operate. 

Static Balance Device 


The static balance device shown in Figure 9-4 (Chapter 9) is nothing more 
than a torsional pendulum. A cross- section drawing of the device is shown 
in Figure C-l. The outside dimensions of the device are 2.625 inches long, 
0.75 inches high, and 0.50 inches wide. The steel wire (0.01 dia.) extends 
about 2 feet on either end from the carriage, and is placed under tension. The 
wire was made from a steel guitar string. The carriage is made of aluminum 
and the sides are highly polished to reflect a light beam. The axial hole is 
first drilled through the aluminum block, and polished so that the bullet makes 
a close slip fit in the hole. The end holes are enlarged to accept the wire end 
fittings at this point. The end fittings are made to have a close fit with the 


Rifle Accuracy Facts 


Figure C-1 - Drawing of the static balance device. 

holes. Then the top of the carriage is milled away, and the edges deburred. 
The silver solder beads on the ends of the wires are formed by holding the 
wire in a vertical position, and melting a small drop of solder onto the end of 
the wire. Gravity will cause the drop to form a perfect tear drop shape. The 
0.032 thick aluminum damping vane is epoxy bonded to the carriage. The 
vane travels between two small magnets placed on both sides of the vane 
near the end of the vane. The brass balance weight is adjusted so the CG of 
the device is near the centerline of the bullet. The carriage will rotate first to 
the right and then to the left as an unbalanced bullet is rotated in the carriage. 
This rotation is detected by shining a light beam onto the highly reflective 
side of the carriage, which when reflected provides a spot of light on a screen 
placed in a perpendicular direction some 20 feet away. The up and down 
excursion of the light spot is measured to determine the amount of CG offset. 
The light beam can be formed by shining a small, high intensity light into the 
eyepiece of a rifle scope. 


I mount the device in a lathe, because it is a stable, convenient way of hold- 
ing it. The wire supports must be stretched tight, so that the carriage does not 
sag. The higher the CG of the carriage is, the greater the sensitivity. How- 
ever, if one raises the CG of the device too high, it will become unstable and 
dump the bullet. To check the balance of a bullet, the bullet is rotated about 


Appendix-C: Bullet Balance Device Design 

45° at a time, and the position of the light spot is noted. The maximum up 
and down excursion of the spot is recorded, and can be converted to CG 
offset in inches by multiplying the result times a calibration constant. The 
calibration constant is determined by drilling a radial hole halfway through 
the bullet at the longitudinal CG position. The CG offset of the calibration 
bullet is easily calculated, and should be large enough (i.e. 0.001 inch) to 
overwhelm any existing CG asymmetry before the hole was drilled . A more 
accurate approach is to make a brass cylinder that has the same weight as the 
bullet to be tested, and drill a hole in it to unbalance it. That way the possibil- 
ity of picking a badly balanced bullet for a calibration bullet is avoided. I 
used a well balanced bullet obtained from the dynamic balancer described 
below. The calibrated sensitivity of this particular device, for an 18 foot 
optical path length, is 0.02 mils per inch of total spot deflection. That is, the 
total spot deflection is the deflection between highest and lowest positions of 
the light spot. Figure C-2 shows the results of balancing the same 100 bullets 
that are balanced with the dynamic balancer described below, and it can be 
seen that while the general result is the same as that obtained from the dy- 
namic balancer, the static balancer results are not as smooth. 

Figure C-2 - Measured center of gravity offset of 100 bullets obtained from the 
static balance device. 


Rifle Accuracy Facts 





A < i - > B 







Figure C-3 - Drawing of the dynamic balance device showing the air passageways 
that allow the bullet to be suspended and spun on an air cushion. 

Dynamic Balance Device 


The bullet dynamic balance device design is based on the use of air bearings 
to constrain the bullet as it spins at a high speed (=150 cps). A photograph of 
the balance device is shown in Figure 9-6 (Chapter 9), and a cross-section 
sketch is shown in Figure C-3. The sketch is not drawn exactly to scale. The 
device is made of polystyrene (plexiglass), a transparent plastic, to facilitate 
drilling all the air passages. Machining must be done at a slow rate with 
water coolant to prevent melting of the plastic. There are two air bearings 
involved. One air bearing supports the base of the bullet, and the other pro- 
vides lateral support along the sides of the bullet and provides the spin ac- 
tion. Air enters the bottom of the device through a small orifice and spreads 
laterally until it exits through the six equally spaced vent holes near the sides 
of the cavity. This air cushion, between the base of the cavity and the base of 
the bullet, lifts the bullet a few mils preventing contact between the base of 
the bullet and the device. The high pressure air in the circumferential 
chamber squirts through the eight equally spaced radial holes (0.016 inch 
dia.) and flows out through the six base vents (.052 inch dia.) and the top of 


Appendix-C: Bullet Balance Device Design 

the cavity. The air in the circumferential chamber is supplied through two 
diametrically placed holes (0.052 inch dia.) into the air supply passage (0. 1 25 
inch dia.). One of these supply holes is shown in Section B. The other 
passage into the circumferential chamber cannot appear in Section A. The 
eight radial holes are drilled parallel to the diameter, but are offset laterally 
about 20 mils to provide the spin action. This offset is not shown in the 
sketch. The cylindrical cavity for the bullet is tapered slightly, measuring 
0.279 inches at the bottom and 0.282 inches at the top for a bullet diameter of 
0.277. This taper greatly improves vertical stability of the bullet. The taper 
is obtained by hand finishing with fine emery paper and finally polishing 
with a fine polishing compound on a wood dowel. I have found that tooth 
paste makes a good polishing compound. The device should be designed so 
that the CG of the bullet will be half way in the vertical direction between the 
two mounting posts that connect to the earphone diaphragms. The posts are 
bonded to the diaphragms with epoxy cement. The two plastic cylinders are 
bonded with plastic cement. The outside diameter of the external cylinder is 
0.65 inches, and the height of the outside cylinder is 0.60 inches. The reader 
is cautioned that the dynamic balance device requires careful machine work 
on good equipment to be successful. The earphones are of the old magnetic 
type, and do not require any electrical power. 


A dual sweep oscilloscope is required if one wishes to measure principal axis 
asymmetry, however a single sweep oscilloscope is sufficient to measure CG 
offset. The oscilloscope is required to check the spin frequency, because the 
voltage output is proportional to the square of the spin frequency. Usually, 
the frequency of reasonably well balanced bullets will be very consistent, 
and all one has to do is check to be sure. Badly balanced bullets, such as 
those used in calibration, may not spin as fast as the regular bullets, and the 
voltage will have to be increased by the square of the spin rate ratio. A 
calibration bullet, or bullets, are made by finding a well balanced bullet and 
drilling a small radial hole to the center line at the longitudinal CG position. 
The edge of the hole must be carefully deburred. In the data shown for the 90 
grain Sierra 270 bullet (Figure C-4), a hole diameter of 0.065 inches provides 
a 1 mil offset, which is as large an offset that one should try. In practice the 
oscilloscope is used to check the spin frequency and a digital multimeter set 
on AC is used to measure the voltage. The calibration of this device yielded 
0.508 volts (RMS) per mil of CG offset, which is a convenient level. The 


Rifle Accuracy Facts 

Figure C-4 - CG offset data for 100 bullets obtained from the dynamic balance 
device compared to a standard Gausian distribution. 

operator has to be careful to allow plenty of time for the bullet to spin up to a 
steady state level (143 cps). This may require as much as two minutes, so it 
is a slow process. In practice the spin rate will usually over speed at first, 
then oscillate and gradually come to a steady rate. If the spin rate is not 
steady the inlet air pressure may be a little too high. In this case the bullet is 
rising and falling in the chamber. With experience, one can usually tell when 
the spin rate has reached equilibrium by simply listening to the high pitched 
hum that the device generates. I use a parallel-jaw machinist clamp on the 
rubber inlet tube to adjust the air flow that comes from the compressor, which 
is regulated at 40 psi. A small air compressor is sufficient to provide enough 
high pressure air. Obviously, the bullets and the chamber must be kept clean, 
because the clearance between the sides of the bullets and the chamber are 
small. In all probability the voltage output of the two earphones will not be 
equal, because the sensitivity of earphones vary. Simply adjust one of the 
traces so that both signals are identical. The voltage output of the two ear- 
phones are exactly 1 80 degrees out of phase. If one sums these two voltages, 
the difference voltage will be proportional to the principal axis asymmetry. 
This means, of course, that the oscilloscope must have at least one summing 
amplifier if principal axis tilt is to be measured. After working with this 


Appendix-C: Bullet Balance Device Design 

device for a long time I have never seen a significant principal axis asymme- 
try. I believe this is inherent in bullet production methods. The principal 
axis, which is coincident with the CG, is just shifted laterally without being 
rotated with respect to the center line axis, or axis of geometrical symmetry. 
This probably results from unequal jacket thickness from side to side. Con- 
sequently, the reader may not want to bother with trying to measure the prin- 
cipal axis asymmetry. 

Resonance between the bullet spin rate and the lateral oscillation frequency 
of the device is one thing that should be guarded against, because resonance 
effects may cause an error. However, the damping of the earphones is very 
large, which inhibits resonance effects. The natural frequency of the device 
can be determined by simply tapping the side of the device and watching the 
output on the scope. I found in this case that the frequencies were a little to 
close, so I wrapped a 1/2 inch wide strip of 1/16 inch thick sheet lead around 
the cylinder between the two support posts. This lowers the frequency of the 
device sufficiently to avoid resonance after spin up has occurred. 

Rifle Accuracy Facts 




T he first Six Degree Of Freedom (6DOF) computer code was developed 
by NASA around 1 960. These early 6DOF codes required long comput- 
ing times on large main frame computers. These days they can be run effi- 
ciently on personal computers with clock speeds of 20 MHz or faster. The 
6DOF code computes the trajectory of a projectile exactly, provided that the 
aerodynamic coefficients and the mass characteristics are accurately known. 
However, they should be operated by experienced flight dynamicists for reli- 
able results. The 6DOF code allows the projectile to rotate and translate in 
three mutually perpendicular planes. These are all the possible components 
of motion, consequently the motion is rigorously defined by the equations. 
Most of the trajectory data that is published for rifle bullets comes from a 
very simple point mass computer code, which completely ignores rotation of 
the bullet. This automatically eliminates the effects of bullet asymmetries, 
spin, and transient motion, and consequently, the point mass trajectory codes 
are useless for accuracy studies. The point mass approach is adequate for 
determining mid-range trajectory height and velocity at various ranges, which 
is helpful to the shooter. The point mass approach is also much faster and 
vastly easier to use as a result of its simplicity. Since we are going to 
investigate the effect of several things on external ballistic accuracy 
(see Chapter 10), the 6DOF code is required. 

Rifle Accuracy Facts 

Equations Of Motion 

The 6DOF code works by solving six equations of motion which describe the 
way the bullet behaves in the six degrees of freedom. This particular code 
can be simplified by making the assumption that the trajectory angles are 
small. The trajectory angles are small for a bullet trajectory over short ranges 
(i.e. 300 yards or less). Also, it is assumed that the aerodynamic coefficients 
are constant with Mach number, which is also true for the typical supersonic 
rifle bullet over reasonable ranges. Both of these simplifications speed up 
the computation. 

The three equations that describe the rotational motion about the roll (x), 
pitch (y), and yaw (z) axes are 

dp/dt = Mx/Ixx 

dq/dt = (-p*r*Ixx + My)/Iyy 

dr/dt = (p*q*Iyy + Mz)/Izz 

where p,q, and r are the roll, pitch, and yaw angular rates, Mx, My, and Mz 
are the roll, pitch, and yaw aerodynamic moments, and Ixx, Iyy, and Izz are 
the moments of inertia of the bullet about the roll (x), pitch (y), and yaw (z) 
axes. The quantities on the left side of the equations are the angular accelera- 
tions about the roll, pitch and yaw axes. When integrated these accelerations 
provide the angular rates of the bullet (p, q, and r), and when integrated a 
second time provide the three attitude angles of the bullet. 

The three lateral translational equations that act along the three roll (x), 
pitch(y), and yaw(z) axes are 

du/dt = r*v - q*w - g*sin0 + Fx/m 

dv/dt = r*tan@*w - r*u + Fy/m 

dw/dt = q*u - r*tan0*v + g*cos0 - Fz/m 

Appendix-D: Six Degree of Freedom (6DOF) Computer Code 

where du/dt, dv/dt, and dw/dt are the translational accelerations, and Fx, Fy, 
and Fz are the applied forces acting along the x, y, z axes. The m is mass of 
the bullet. If the bullet is launched in a near horizontal direction, so that the 
pitch angle 0 is small and the range is not too large (300 yards), these equa- 
tions simplify to 

du/dt = r*v - q*w -g*0 + Fx/m 
dv/dt = r*0*w - r*u + Fy/m 
dw/dt = q*u -r*0*v + g - Fz/m 

These three accelerations can be integrated to provide the velocities along 
the three axes. These velocities can be used in the following equations to 
determine the flight path of the bullet relative to an earth fixed coordinate 

dXe/dt = u*cos0*cosr - v*sinT + w*sin0*cosr 
dYe/dt = u*cos0*sinT + v*cosT + w*sin0*sinr 
dZe/dt = -u*sin0 + w*cos0 

The translational equations can be simplyfied for small angles and are 

dXe/dt = u - v*T + w*0 
dYe/dt = u*r + v + w*0*T 
dZe/dt = -u*0 + w 

These simplifications are only desirable when using the older personal com- 
puters (PCs), such as the Z80 and the 80186 without a coprocessor. The 
three Euler angles in roll, pitch and yaw (0, 0, and T) are obtained by inte- 
grating the following angular rate equations. 

dp/dt = -r*tan0 
d©/dt = q 
dT/dt = r*sec0 

These angular rate equations can be simplified to 

d0/dt = -r*0 
d0/dt = q 
dT/dt = r 


Rifle Accuracy Facts 

A fourth order Runge-Kutta integrator is used for integrating all equations. 
The aerodynamic angle of attack and angle of sideslip are required for deter- 
mining the aerodynamic forces and moments in the six equations. These are 

a = arctan(w/u) 

8 = arctan(v/u) 

The aerodynamic force and moments must either be calculated or obtained 
from experimental data. In general I have used experimental aerodynamic 
and inertial data in calculating the external ballistics for this book. A mini- 
mum of two force coefficients and four damping coefficients are required in 
the case of a rotationally symmetric projectile. I think I have gone about as 
far as possible in explaining to the average reader how these complex calcu- 
lations can be made. The 6DOF computer code will tell you in great detail 
how a bullet will fly, if you have the correct aerodynamic and inertial data, 
and the correct launch conditions. This has been proven over and over by 
flight tests. 




A fter fighting with wind drift problems for years and finding it difficult 
to separate wind effects from other accuracy problems, I decided to 
build a Tunnel Range to eliminate wind effects. With the approval of the Zia 
Rifle and Pistol Club of Albuquerque we built it on the Club Range. The club 
purchased enough used four foot inside diameter concrete pipe to make a 100 
yard range for five hundred dollars. My son and son-in-law laid in railroad 
ties which were surveyed with a rifle scope on a tripod to within 1/2 inch. 
The ties were placed about six feet from the ends of each section of pipe. 
Most of the pipe sections were 34 feet long and weighed about 12 tons each. 
I rented two 30 ton cranes and one flatbed truck for $1700 - one crane for 
loading at the salvage yard and one for unloading at the site. A cross was 
made of 1 x2 lumber that would fit in the far end of the pipe and was used as 
a crosshair for alignment. This worked very well. The final alignment re- 
quired one inch shims on only two ties to bring the centers of the pipe sec- 
tions within one inch of alignment throughout its length. Tapered chocks, 
made from 6x6 lumber, were driven between the railroad ties and the pipe to 
prevent any motion of the pipe. The chocks were nailed in place with large 
nails. Figure E- 1 shows the range before being covered with about 500 cubic 
yards of dirt to maintain thermal equilibrium. An 11x15 foot concrete slab 
was poured at the entrance end of the tunnel and a building constructed on 
the slab. The forward end of the building is made of concrete block and acts 
as a retaining wall for the dirt covering. A photo of the finished range is 


Rifle Accuracy Facts 

Figure E-1 - Tunnel Range showing exposed pipe before covering with earth. 

shown in Figure E-2 and a view of the interior of the building is shown in 
Figure E-3. The outside of the 2x4 structure is covered with 3/8 inch ply- 
wood. The roof of the building is covered with corrugated translucent fiber- 
glass. In the summer 4x8 foot sheets of thin white polyethylene foam are 
nailed to the bottom of the ceiling rafters to provide shade. A 3.5 inch thick 
shooting bench was made of reinforced concrete poured in place on the con- 
crete filled concrete block pedestals. However, we found the concrete block 
pedestals too unstable and later replaced them with one foot diameter solid 
cast concrete pedestals. The pedestals were cast in commercial cardboard 

Figure E-2 - Finished range. Louvered inlet for fan is to the right of the door. 


Appendix-E: Tunnel Range Construction 

Figure E-3 - Photo of the interior of the building showing concrete bench and 
entrance of the 100 yard tunnel. 

forms and proved to be perfectly rigid. The building was wired for electric 
outlets and lights. A target light was installed. This made it possible to con- 
duct the muzzle blast studies at night. A loading table is shown on the left 
and an adjustable stool is by the bench. There is a gate at the muzzle end that 
serves to keep out trash when the tunnel is not in use and is locked in the open 
position to prevent people from wandering in between the target butt and the 
tunnel muzzle. All of the muzzle end, with the exception of an opening for 
the muzzle gate, is surrounded by a berm. The target is seven feet from the 
muzzle end of the tunnel, which allows room for a chronograph. The bench 
was placed so that the rifle muzzle would be about six feet from the tunnel 
entrance. The Oehler 35P chronograph gates with lights are placed inside 
the mouth of the tunnel on short stands made of 2X4 lumber. There is a 
louvered opening to the right of the building door that conceals a 30" diam- 
eter exhaust fan. This facility has proved to be a very nice tool, however 
mirage has proven to be a problem. 

Before building the tunnel range I had talked to several people with some 
experience with them, but no one seemed to say much about mirage prob- 
lems, which proved to be nearly as bad as the wind. The first time three of us 
tried firing in it we all got groups with nearly pure vertical dispersion. 


Rifle Accuracy Facts 

When we watched through the scope we could see the reticule move up or 
down over a total distance of as much as 0.6 inches. One of the shooters (Bill 
Minneman), that I had talked to, mentioned that he had installed an exhaust 
fan to reduce the mirage effect, so I tried installing a fan that pulled the air 
from the muzzle end toward the entrance at a rate of about 7 feet per second. 
The fan reduced the slow mirage drift by about a factor of three 



30 40 50 60 70 80 


























Figure E-4 - Graph showing variation of Tunnel wall temperature for the 
months of the year. 


Appendix-E: Tunnel Range Construction 

(i.e., 0.2 inch), which is still too much when you are trying to test a rifle that 
shoots in the ones and twos (i.e., 0. 1 to 0.2 inch groups). I found that it 
worked much better if the air was forced down the tunnel, which meant seal- 
ing the building. Meanwhile I had been measuring the tunnel wall tempera- 
ture (Figure E-4) and found that if one matched the outside free air tempera- 
ture with the tunnel wall temperature the mirage disappeared. A thermom- 
eter was hung on the shady side of the building to indicate free air tempera- 
ture and a copy of Figure E-4 was posted in the building. Since we are in a 
desert climate, the tunnel wall temperature change from winter (49°F) to 
summer (80°F) is much larger than you would expect in some climates. The 
tunnel temperature essentially follows the average daily temperature. Before 
turning on the fan the top and bottom wall temperatures usually differ by 3°F 
to 4°F. After the fan has run for 30 minutes the surface temperatures at the 
top and bottom of the tunnel seem to reach equilibrium. On the Pacific coast 
the seasonal temperature doesn’t vary much and one should have less trouble 
with mirage. The next improvement was to build a reference scope mount 
(Figure F-l) that holds a scope with the reticule initially fixed on the aim 
point as a reference. The rifle scope is then aimed at the same point that the 
reference scope indicates should be the true aim point without mirage. My 
experience indicates that with the fan on and the temperatures matched within 
5°F the correction due to mirage is less than 20 mils on the target while firing 
a single group. This seems to have solved the mirage problem. The reference 
scope mount holds the reference scope at the same level as the rifle scope and 
about two inches to the left, so that the shooter can move rapidly back and 
forth between scopes for comparison. I also tried projecting a laser spot on 
the target that was about 0.25 inches in diameter at the target and shooting at 
the laser spot. However, this was not too successful because scintillation caused 
the spot to twinkle like a star and made aiming difficult. With a rail gun that 
holds its zero between shots a reference scope really isn’t necessary. How- 
ever, I usually use the reference scope because it not only checks mirage 
conditions but tells you if the rail gun has moved between shots. 

The Tunnel Range may not work for transonic velocity (1000 to 1500 fps) 
projectiles because the normal shock waves will be reflected back from the 
tunnel walls to the bullet. This can cause instability of the bullet with large 
dispersion. We know that it doesn’t work for low or medium large caliber 
bullets such as muzzle loader or pistol bullets, because we have seen oblong 
bullet holes in the target. However, it may work for 22 RF if the trajectory is 


Rifle Accuracy Facts 

in the center of the tunnel and low speed match ammunition is used. The 22 
may be small enough compared to the tunnel inside diameter that the shock 
waves could be too weak to effect the bullet. A tunnel range is just not worth- 
while for anything but accurate guns. 

If I built another one of these ranges about the only thing that I would change 
would be to place the fan in the middle of the building so that it lined up with 
the tunnel center line. Since the fan is off center, it tends to generate a swirl- 
ing motion of the air about a vertical axis in the building, which may cause 
some dispersion. I might also consider placing a vertical baffle between the 
fan and the rear of the bench, because it gets cold sitting in the draft when the 
outside temperature drops below 55°F. One might also consider building a 
small building at the muzzle end of the tunnel for safety reasons. We had to 
build this range so that it pointed toward the south to conform to the Zia 
Range layout. Unfortunately, the wind often is out of the south or southwest 
which interferes with the flow induced by the fan. It would be best to orient 
the tunnel to point in a direction parallel to the prevailing wind. We only 
have an annual rainfall of 8 inches, so drainage is not a problem. 

I have found the Tunnel Range to be essential in doing rifle accuracy diag- 
nostic work because it eliminates the worst variable - wind effects. As far as 
mirage effects are concerned they are present on an open range but shooters 
are often unaware of them. The tunnel range exaggerates mirage effects but 
by using the fan and matching free air and tunnel wall temperatures the mi- 
rage is effectively eliminated. However, one should use the reference scope 
to be sure of the mirage conditions. 

I have made a mount to hold a sporter stock, which was shown earlier in 
Chapter 2 (Figure 2-2). It was not as accurate as a regular rail gun but 
served its purpose of holding the instrumented sporter. I decided I needed a 
rail gun for testing in the Tunnel Range and the gun shown in Figures F-l and 
F-2 was the result. Also shown in Figure F-l is a reference scope and mount 
for the reduction of mirage problems. Both scopes are 36X Bauch and Lomb. 

Figure F-1 - Photograph showing the left side of the rail gun and the mirage scope 
on a separate mount. Note counterweights fastened to the barrel block. 



Rifle Accuracy Facts 

Figure F-2 - Photograph of the right side of the rail gun. 

I started out with a used gun to save time and money. On the original gun the 
front “T” shaped bearing mount was on a separate tripod and the rear adjust- 
ment mount was on a separate plate. I mounted both of these on a 3/4" thick 
aluminum base plate, which made the gun a lot more rigid. The Bakelite and 
Delrin bearings were replaced with Teflon, which I consider much superior. 
The measured static friction coefficient with the Teflon bearings was 0.025, 
which is very low. The foot screws are 1/2" diameter and are secured with 1/ 
4" cap head set screws. Carbide inserts from 30 caliber armor piercing bul- 
lets are silver soldered into the end of the foot screws. These carbide inserts 
are hard and sharp enough to penetrate a concrete bench top with a gentle tap 
from a small hammer, so they stay put. The procedure in setting the base is to 
set the front of the base on two short pieces of 1 x2 wood and move the base 
until the sight is pointed at the aim point. Then the two front foot screws are 
turned until the front of the base is level and above the two wood blocks. 
Then the lock nuts on the two foot screws are tightened and tapped into the 
bench with a small hammer, the next step is to tighten the set screws that 
lock the foot screws. The procedure is repeated on the rear foot screw. 
The rails are cleaned and lubricated with Pledge, a furniture polish 
or Friction Block. 



Appendix-F : Rail Gun 

Figure F-3 - Photograph of the rear of the rail gun showing details of the windage 
and elevation adjusting mechanism. 

The original windage and elevation adjustment on the rear of the gun was 
unsatisfactory and was modified to prevent movement between shots. A photo 
of the final adjustment system is shown in Figure F-3. The 3/4 inch steel 
adjustment plate is hinged with a close fitting 3/8 inch diameter steel rod 
toward the front of the plate. The capstan wheel underneath the rear of the 
plate provides elevation adjustment and the two screws on either side provide 
windage adjustment. There are two vertical hex head bolts at the front of the 
adjustment plate that stabilize the plate by providing a preload. The proce- 
dure is to aim the rifle about two inches above the intended aim point then 
tighten the two hex bolts finger tight and raise the rear of the adjustment plate 
with the capstan wheel until the elevation is correct. The horizontal adjust- 
ment is done with the two horizontal screws and both are tightened. As far as 
I can tell this gun does not move between shots and with a 36 power scope 
you can detect very small movement of the reticule. If there appears to be 
any movement I check for mirage effects by comparing the mirage scope 
position to the rifle scope. In this way you know whether the gun has moved 
or you are observing a mirage effect. 

I tried several different barrel block designs and finally settled on aluminum 
V-blocks as being the best. These different methods included steel V-blocks, 


Rifle Accuracy Facts 

aluminum blocks with circular cuts to match the barrel, and epoxy bedding. 
The bottom block is bedded in Devcon F epoxy and is held by six 3/8 inch 
bolts. The position of the blocks is adjusted with shims until the carriage can 
be moved all the way with no more than 1 mil variation on a dial gage at- 
tached to the base. Six 3/8 inch bolts clamp the top and bottom blocks to- 
gether and are torqued to 50 inch pounds. The V-block surfaces are coated 
with a solution of rosin in acetone to prevent any possibility of movement. 

There are 3/4x4x7 inch steel blocks bolted to both sides of the top barrel 
block (Figure F-2). These are counterbalance weights that counteract the 
recoil moment caused by the recoil force acting on the blocks. When the gun 
is fired the rearward recoil force is opposed by the forward inertial force 
acting on the carriage. These two forces cause a couple (moment) tending to 
rotate the barrel blocks and the barrel in a muzzle upward direction. The 
forward inertial forces acting on the two counterweights acts to compensate 
the recoil moment reducing the moment acting on the barrel. This was deter- 
mined by measuring the moment acting on the barrel just forward of the 
barrel blocks with strain gages. Figure F-4 and F-5 show the measured 


Figure F-4 - Computer scan of oscilloscope data on rail gun barrel moment without 
counterbalance weights. 


Appendix-F: Rail Gun 

Figure F-5 - Computer scan of oscilloscope data showing rail gun barrel 
moment with counterweights. When compared with Figure F-4 it can be seen 
that the weights greatly reduced the moment acting on the barrel, thereby 
reducing vibration. 

moments with and without the counterbalance weights. You can see that the 
moment is reduced to near zero with the counterweights. This greatly re- 
duced the vertical stringing that was present in the groups without the weights. 
See Chapter 4 for a discussion of high frequency vibration problems ob- 
served on this gun. 

There is a 1 .875" OD aluminum tube that covers the barrel ahead of the bar- 
rel blocks. This tube, which was suggested by Frank Tirrell, helps to main- 
tain a constant circumferential temperature of the barrel which minimizes 
thermal distortion and shifting of point of impact due to differential cooling. 

About the only thing that I can think of to improve this gun would be to lower 
the carriage so that it is closer to the base plate. It has proved to be a very 
handy tool for evaluating ammunition problems. The carriage and the base 
each weigh approximately 45 pounds. 

If I were to build one of these things from scratch I would consider using 
flexures like those used on the Recoil Isolator in Chapter 4 instead of 

Rifle Accuracy Facts 

bearings. The carriage only has to recoil about 0.010 inches before the bullet 
exits the muzzle which should be easy to accommodate with flexures. The 
recoil could be absorbed by an adjustable hydraulic damper. However, the 
amount of horizontal windage adjustment might be somewhat limited. I would 
also try to design the carriage so that the CG of the carriage plus barrel 
and action would end up on the bore line. This would prevent some 
vibration problems. 



S hadowgraphs have been used for years in diagnostic testing in ballistic 
ranges and wind tunnels. A high intensity, short duration beam of light, 
usually from an arc light source, is passed through the flow region of interest 
and a shadow of the flow is cast on a sheet of fdm which is exposed. The 
image shows significant density gradients such as turbulence and shock waves. 
It allows an investigator to really see a physical picture of the flow region. 

I should warn the reader that the high voltage and energy involved in the 
arc light source is exceedingly dangerous and very likely will kill you if 
you accidentally contact the high voltage. It is much more dangerous than 
the high voltage in a television set because of the high energy involved. So, 
1 advise against duplication of this equipment unless the reader is experi- 
enced in working with high voltage equipment. 

Figure G-l shows the equipment setup with the rail gun in the Tunnel Range. 
The white box in the foreground contains the high voltage supply and the 
trigger electronics. In the background on the right side you can see the arc 
head, which is enclosed in a Nylon box. The Nylon knob on the right hand 
side of the arc head adjusts electrode spacing. The microphone is visible near 
the muzzle that triggers the electronics. On the left side of the gun a black 
screen can be seen. The 12"xl8" lithograph sheet film is clamped to the 
black screen. The round black device in front of the box containing the 


Rifle Accuracy Facts 

Figure G-1 - Photograph of the shadowgraph equipment set up in the Tunnel 
Range with the rail gun. The round object in the foreground is a variac that adjusts 
the line voltage feeding the high voltage power supply. The white cabinet on the 
right contains the electronic circuitry. Behind the white cabinet is the arc light. 

The black board on the left holds the lithographic film. 

electronics is a variac, which adjusts the line voltage to the high voltage power 
supply. The high voltage is indicated by the microammeter on the right front 
of the electronics box. 

The spacing between the arc head and the muzzle is about 12" and the dis- 
tance between the muzzle and the fdm screen varies from 4" to 10" depend- 
ing on whether the large sheets of lithographic film (12"xl8" Fuji GA-100) 
or Type 57 Polaroid 4x5 film is used. The 4x5 camera using the Polaroid 
film is mounted above and behind the arc head. The Polaroid film is exposed 
at f-4.5 and is useful in checking the result, but not very good for reproduc- 
tion. You can quite often see the image with the eye well enough without 
photography to tell whether are not the timing is correct. The lithographic 
film is developed in Kodak Tmax developer for 7-10 minutes. The photo- 
graphs shown in the book were made by photographing the 12"xl8" film 
negatives on a light table with Tmax 100 film in a 4x5 camera and then re- 
versing with a Kodak Tmax 100 reversal developing kit. The resulting nega- 
tives were printed. 


Appendix-G: Shadowgraph Testing 

Figure G-2 shows a front view of the setup, showing the trigger microphone 
near the muzzle for late time shots. Figure G-3 shows the hole in the 
side of the barrel used for early time shots. The hole is 3/16"D at the surface 
and the last 0.05" is 1/1 6"D. The hole is 5.5 inches from the muzzle. 

Figure G-2 - View of the side of the barrel showing the microphone at the muzzle 
and the hole in the side of the barrel for early time triggering. The microphone is 
placed near the hole for early time triggering and the time adjusted by moving the 
microphone away from the barrel for more time delay. 

Figure G-3 - Front view of the shadowgraph setup, showing the arc light source on 
the left and the film mounting board on the right. The microphone is placed near the 
muzzle for late time shots. 


Rifle Accuracy Facts 

You can see where the powder smoke has discolored the white surface of the 
gun carriage. Put some kind of baffle between the hole in the barrel and the 
operator to avoid being hit in the face by powder fragments. 

The total time delay in this system averages about 0. 1 msec. Most of the time 
delay is in the reed relays in the flip flop circuit. To operate, one pushes the 
reset button and a red LED will come on indicating the unit is ready to fire. 
When the microphone receives a sound pulse it is amplified and triggers a 
flip flop. The flip flop controls a power transistor which controls the primary 
circuit in an auto ignition coil. This collapsing field in the primary of the 
ignition coil induces a high voltage in the secondary, which is connected to 
the trigger arc electrode in the arc head. When the trigger arc fires this causes 
the main arc to fire and discharge the capacitor bank in the arc head. When 
the unit fires a yellow LED comes on indicating the unit is on standby. If the 
unit is left in the ready condition too long the high current (3 amps) may 
cause the power transistor and the ignition coil to overheat. The unit can be 
fired manually by pushing the test button when the red LED is on (ready 
position). The microphone is a small capacitor type purchased from Radio 
Shack. The arc head design is an adaptation of a design used at Sandia Na- 
tional Laboratory which was furnished by Dr. Ken Cole. Commercial ver- 
sions of this device are available from EG&G Electro-Optics, Salem, MA 

The discharge time of this device is about 0.5 psec, but since most of the light 
energy comes out in about 2/3 that time the effective light pulse is about 0.32 
psec. The bullet moves about 0.012 inches in that time. So the motion is 
effectively stopped. The high voltage supply is 10 kv that charges six 0.02 
mfd capacitors in parallel. Again, do not trust the insulation or the 
current bleed circuit to make this thing safe. It is deadly!!!! 






ballistic coefficient 




bullet seating depth 

The response of a body to an applied force. 

The ability of rifle to fire bullets into a target 
near the aim point. 

The rear portion of a bullet shape that starts 
just behind the nose section. May include a 
boat tail. 

The ratio of the bullet mass to a function of the 
aerodynamic drag force. 

Erratic side to side or angular motion of a 
projectile in a gun bore. 

Refers to the rearmost surface of a bullet. 

Powder gasses that travel around the bullet 
before the bullet enters the bore. 

The depth that the bullet is seated into the case 
neck. Also refers to the depth that the bullet is 
seated into the throat. 



Rifle Accuracy Facts 
burning rate 



coning motion 

center of gravity 


compression stress 

diametrical clearance 

drag coefficient 

dynamic pressure 

expansion shock 

The rate that gun powder burns at a given 
pressure in inches per second. 

The maximum diameter of a bullet in inches 
or millimeters. 

A circumferential groove impressed into the 
afterbody of a bullet. 

The motion a bullet makes with its nose travel- 
ing in a circle while the CG remains fixed on the 
flight path. 

That point in a body where the mass can 
effectively be assumed to be concentrated. 

Also center of mass. 

The cavity in a rifle barrel that contains a 
cartridge up to the start of the throat or leade. 

An electronic instrument that measures the 
velocity of a projectile. 

The force that tries to compress a piece of 
material divided by the area perpendicular to the 
direction of the force. 

Difference in diameter between two concentric 

The coefficient formed by dividing the aerody- 
namic drag force by the dynamic pressure and 
bullet cross section area. 

The pressure caused by the motion of a gas. 
Equal to one half the gas density times the 
square of the velocity. 

The shock wave cased by the lateral expansion 
of the muzzle blast. 



Glossary & Abbreviations 

external ballistics 

extreme spread 


free run 

The study of the flight of a projectile after it 
leaves the influence of the barrel. Also flight 

The difference between the lowest and highest 
muzzle velocities of a group of bullets and the 
dimension between the centers of the widest 
bullet holes in a group. 

Applies to an electronic circuit where some of 
the output current or voltage is fed back to the 
input of the circuit increasing the amplification 

The distance a bullet must travel before it 
contacts the throat in a chamber. 

friction force coefficient The ratio of the force required to slide two 

pieces of material to the force holding the two 
pieces together. 

grain Unit of weight. There are 7000 grains in 

one pound. 

group size The distance between the centers of bullet holes 

that have the largest spread in a group. 

Also precision. 

headspace The space between the face of the rifle bolt and 

the head of the cartridge case. 

Heavy Varmint (HV) rifle A bench rest target rifle weighing up to 

13.5 pounds. 

heel The corner of the bullet at the base. 

internal ballistics The science of predicting the behavior of the 

bullet inside the barrel and the forces and 
stresses on the barrel. 


One thousand cycles per second. 


Rifle Accuracy Facts 

Light Varmint (LV) rifle 


Mach disk 

Mach number 

muzzle ventilation 


normal shock wave 



precursor shock wave 
pressure ring 

radial clearance 

A bench rest target rifle weighing up to 
10.5 pounds. 

The weight of an object divided by the gravita- 
tional acceleration. 

One millionth of a second. 

One thousandth of a second. 

A flat surface shock wave normal to the flow 
velocity where the flow is Mach one. 

The ratio of velocity to the speed of sound in a 
gas. Named for Professor Mach in the 1930’s. 

The practice of drilling holes in a barrel near the 
muzzle to relieve the muzzle blast pressure. 

The product of a force times the distance 
between the force and point of application 

A planar shock wave that forms perpendicular to 
the direction of the gas flow. The flow behind 
the shock wave is Mach one. 

An electronic instrument that displays the 
variation of a signal voltage on a cathode ray 
tube similar to a television tube. 

An optical problem in a telescopic sight where 
the image appears to move when the eye is 
moved off the optical axis of the scope. 

A shock wave formed at the muzzle by the 
compressed gas traveling ahead of the bullet. 

A small oversize ring on the heel of some 
bullets produced during manufacture. 

Difference in Radius between two 
concentric circles. 


Glossary & Abbreviations 

rail gun 

run out - (RO) 

secant ogive 


shock wave 


strain gage 

tangent ogive 

tension stress 

A rail gun has a barrel and action clamped to a 
carriage which slides on rails that ride on 
bearings. They usually are heavy (100 pounds) 
and are used for test purposes, although they are 
used in bench rest unlimited class competition. 

The measurement taken on the surface of a 
cylinder with a dial gage that is rotated about 
a longitudinal axis not necessarily on its 
center line. 

A bullet nose shape generated by a segment of a 
circular arc that is not tangent at its intersection 
with the afterbody. 

The practice of shining a high intensity short 
duration light through a flow field onto a sheet 
of film to get a photograph of the flow including 
shock waves. 

A shock wave represents a sharp discontinuity in 
pressure, density and temperature that travels 
through a gas (air). A sound wave is a very 
weak shock wave that travels at the speed of 
sound in air (1160 fps). The pressure, density 
and temperature is higher behind the wave. 

Unit of mass - pounds/gravitaional 
acceleration (G) 

A thin metal foil that changes electrical resis- 
tance when stretched allowing a measurement 
of strain. 

A bullet nose shape generated by a circular arc 
section where the arc is tangent to the afterbody. 

The force that tries to stretch a piece of material 
divided by the area perpendicular to the 
direction of the force. 


Rifle Accuracy Facts 

thermistor An electrical resistor that changes electrical 

resistance with a change in temperature. 

throat The tapered entrance just ahead of the chamber 

where the bullet enters the barrel. Also, leade. 

transition ballistics The study of the behavior of a projectile as it 

leaves the muzzle of a barrel but is still in the 
influence of the muzzle blast. 

twist rate The distance along a barrel that it takes for the 

rifling or a bullet to make one revolution. 

ultimate strength (stress) The stress where a piece of metal breaks. 

yield strength (stress) The stress level where a piece of metal starts 

failing and will no longer return to its original 
shape when the load is removed. 




G org 













cycles per second 
feet per second 

acceleration of gravity, 32. 1 6 feet per second'' 
kilocycles, thousands of cycles per second 
millimeter, 1/1000 of a meter, 1/25.4 inch 
one thousandth of an inch 
milliseconds, one thousandth of a second 
radian, equals 57.3 degrees 

microsecond, one millionth of a second 
degrees Fahrenheit 
degrees centigrade 

degrees Rankine - degrees Fahrenheit + 459.6 
center of gravity 
gyroscopic stability factor 


1 . “Absolute Chamber Pressure In Center Fire Rifles”, 1965 by Brownell, 
York, Sinderman, Jacobs, and Robins. University of Michigan, 
Ann Arbor, Michigan 

2. “Theory Of The Interior Ballistics Of Guns”, 1950 by Corner. 
John Wiley and Sons, New York. 

3. “Gun Propulsion Technology”, Vol. 109 Progress in Astronautics and 
Aeronautics, American Institute of Aeronautics and Astronautics, 
Washington, DC 20024 

4. “Pressure Measurements In The Transitional Ballistics Region Of 
AM-16 Rifle”, 1975 by Gion, BRL Report No. 1765, USA Ballistic 
Research Laboratories, Aberdeen Proving Ground, Maryland. 

5. “The Effect Of Muzzle Jet Asymmetry On Projectile Motion”, 1975 by 
Schmidt, BRL Report No. 1756, USA Ballistic Research Laboratories, 
Aberdeen Proving Ground, Maryland. 

6. “The Intermediate Ballistic Environment Of The M16 Rifle”, 1976 by 
Zoltani, BRL Report No. 1860, USA Ballistic Research Laboratories, 
Aberdeen Proving Ground, Maryland. 


Rifle Accuracy Facts 

7. “Investigations Of The Transitional Ballistics In Muzzle Jet Flow 
Simulators”, by Oertel, BRL Report No. 2686, USA Ballistic Research 
Laboratories, Aberdeen Proving Ground, Maryland. 

8. “The Prediction Of Gun Muzzle Blast Properties Utilizing Scaling”, by 
Fansler and Schmidt, BRL Technical Report No. ARBRL-TR-02504, 
USA Ballistic Research Laboratories, Aberdeen Proving Ground, 

9. “Interior Ballistics Of Guns”, 1979, Vol. 66, Progress in Astronautics 
and Aeronautics, American Institute of Aeronautics and Astronautics, 
Washington, DC 20024 

10. “Advanced Gunsmithing”, by W.F. Vickery, 1940, Kingsport Press, 
Kingsport, Tennessee. 

11. “Gunsmithing”, by Roy F. Dunlap, 1950, Small Arms Technical 
Publishing Company, Georgetown, South Carolina. 

12. “Machinery’s Handbook”, 1975, Industrial Press, 200 Madison Ave., 
New York, NY 10016. 

13. “Comparison Of Computed And Measured Jump Of 120mm Cannon”, 
1990 by Schmidt et al, Sixth USA Symposium On Gun Dynamics, 
Taimiment, Pennsylvania. 

14. “Launch dynamics Of Fin-Stabilized Projectiles”, 1989 by Schmidt et 
al, AIAA-89-3395, AIAA Atmospheric Flight Mechanics Conference, 
Boston, Massachusetts. 

15. “Investigations On The Dynamics Of Tank Guns”, 1990 by 
Bornstein et al. Sixth USA Symposium On Gun Dynamics, 
Taimiment, Pennsylvania. 

16. “Flexible Projectile Modeling Using The Little Rascal Gun Dynamics 
Program”, 1990 by Erline et al, Sixth USA Symposium On Gun 
Dynamics, Taimiment, Pennsylvania. 

17. “The Flexure Of A Uniformly Pressurized Circular, Cylindrical Shell”, 
by J.D.Wood, ASMR Journal Of Applied Mechanics, Dec. 1958 (p453) 



18. “An Introduction To The Design And Behavior Of Bolted Joints”, 
J.L. Bickford, 1981, Marcel Dekker Inc., New York, NY 

19. “Mechanical Engineering Design”, J.E.Shigley, 3rd Edition, 
McGraw Hill, p250-252. 

20. “Numerical Investigation Of Inviscid Shock Wave Dynamics In An 
Expansion Tube”, Keun-Shik Chang, Jong-Kwan Kim, Shock Waves 

21. “The Bullets Flight”, Dr.F.W.Mann (1856-1916), Copyright 1909, 
Reprinted 1980 by Wolfe Publishing Co., PO Box 30-30, Prescott, 
Arizona 86302. 

22. “A Detailed Development Of The Tricyclic Theory”, H.R. Vaughn, 1968, 
SC-M-2933, Sandia National Laboratories, Albuquerque, NM 

23. “Free Flight Motion Of Symmetric Missiles”, C.H. Murphy, Ballistic 
Research Laboratories Report No. 1216, 1963, US Army Ballistics 
Research Laboratories, Aberdeen, Maryland. 

24. “The Aerodynamic Characteristics Of The 7.62MM Match Bullets”, 
R.L.McCoy, Ballistics Research Laboratory Memorandum Report BRL- 
MR-3733, 1988, US Army Ballistics Research Laboratories, Aberdeen, 

25. “A Magnus Theory”, H.R. Vaughn and G.E.Reis, 1973 American Insti- 
tute of Aerodynamics and Astronautics Paper No.73-124, AIAA 11th 
Aerospace Sciences Meeting, Washington, DC. 

26. “Walter Watts’ Wind Machine”, Walter Watts, The Rifle Magazine, 
July-August 1969. 

27. “Aerodynamic Data For Small Arms Projectiles”, W.Braun, Ballistics 
Research Laboratories Report No. 1630, 1973, US Army Ballistics 
Research Laboratories, Aberdeen, Maryland. 

28. “Gun Tubes”, US Army Material Command, AMC Pamphlet 706-252. 

Rifle Accuracy Facts 

29. “The Aerodynamic Characteristics Of .50 Ball, API, M8, And APIT, M20 
Ammunition”, R.L. McCoy, 1990, Ballistics Research Laboratories 
Report No.3810, US Army Ballistics Research Laboratories, Aberdeen, 

30. “Design of Op-Amp Circuits”, H.W. Berlin, Howard W. Sams and 
Company, 1984 


The long-awaited successor to the 1909 classic work, 
The Bullet’s Flight, by Dr. Franklin W. Mann - 

A highly-decorated veteran of World War II’s Pacific Theatre, Harold 
_T~ \ Vaughn flew one hundred combat missions in P-47’s and P-51’s and 
lived to look back on his experiences. After the war he joined Sandia 
National Laboratories in New Mexico, duly progressed to Supervisor of the 
Aeroballistics Division, and occupied that lofty position until his retirement 
in 1986. As supervisor of the division, he provided technical direction to a 
large staff of scientists. 

In his spare time in recent years, Mr. Vaughn has been increasingly bothered 
by the question that has haunted American rifle shooters back to 
Revolutionary times . . . why do some rifles shoot much better than others? 
With determination of a type to be expected in a man with his background, 
Harold Vaughn set out to find plausible answers to this enigma. After years 
of experimenting and testing, you, the reader, now hold answers to questions 
that earlier generations of riflemen sought but could never attain. 

Rifle Accuracy Facts